Faraday's law of induction

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situation is analyzed in the article, in which, when writing the integral equations of the electromagnetic field in a four-dimensional covariant form, in the Faraday’s law the total time derivative of the magnetic flux through the circuit appears instead of the partial time derivative. Thus, electromagnetic induction appears either when the magnetic field changes over time or when the area of the circuit changes. From the physical point of view, it is better to speak not about the induction emf, but about the induced electric field strength

1102: 135: 5354: 4853: 958: 4078: 3022: 1005: 107:) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is emf (electromotive force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on a conductive loop when the magnetic flux through the surface enclosed by the loop varies in time. 7513: 22: 5568: 1665: 3575: 2484: 4639: 3803: 2766: 7244: 4295: 3777: 5382: 3403: 3206: 2263: 4848:{\displaystyle (\mathbf {v} \times \mathbf {B} )\cdot \mathrm {d} \mathbf {l} =((\mathbf {v} _{t}+\mathbf {v} _{l})\times \mathbf {B} )\cdot \mathrm {d} \mathbf {l} =(\mathbf {v} _{t}\times \mathbf {B} +\mathbf {v} _{l}\times \mathbf {B} )\cdot \mathrm {d} \mathbf {l} =(\mathbf {v} _{l}\times \mathbf {B} )\cdot \mathrm {d} \mathbf {l} } 4073:{\displaystyle \left.{\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}\right|_{t=t_{0}}=\left(-\oint _{\partial \Sigma (t_{0})}\mathbf {E} (t_{0})\cdot \mathrm {d} \mathbf {l} \right)+\left(-\oint _{\partial \Sigma (t_{0})}{\bigl (}\mathbf {v} _{\mathbf {l} }(t_{0})\times \mathbf {B} (t_{0}){\bigr )}\cdot \mathrm {d} \mathbf {l} \right)} 4424: 3017:{\displaystyle \left.{\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}\right|_{t=t_{0}}=\left(\int _{\Sigma (t_{0})}\left.{\frac {\partial \mathbf {B} }{\partial t}}\right|_{t=t_{0}}\cdot \mathrm {d} \mathbf {A} \right)+\left({\frac {\mathrm {d} }{\mathrm {d} t}}\int _{\Sigma (t)}\mathbf {B} (t_{0})\cdot \mathrm {d} \mathbf {A} \right)} 4082: 3585: 2225: 5258: 1943: 5563:{\displaystyle {\mathcal {E}}=\int _{\partial \Sigma }(\mathbf {E} +\mathbf {v} _{m}\times \mathbf {B} )\cdot \mathrm {d} \mathbf {l} =-\int _{\Sigma }{\frac {\partial \mathbf {B} }{\partial t}}\cdot \mathrm {d} \Sigma +\oint _{\partial \Sigma }(\mathbf {v} _{m}\times \mathbf {B} )\cdot \mathrm {d} \mathbf {l} } 2759: 2626: 3037: 7106:

Note that the law relating flux to emf, which this article calls "Faraday's law", is referred to in Griffiths' terminology as the "universal flux rule". Griffiths uses the term "Faraday's law" to refer to what this article calls the "Maxwell–Faraday equation". So in fact, in the textbook, Griffiths'

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The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest,

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But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the

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appearance by action of the magnetic force on the charges in the moving wire or in the circuit changing its area is unsatisfactory. As a matter of fact, the charges in the wire or in the circuit could be completely absent, will then the electromagnetic induction effect disappear in this case? This

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drives a current along the conducting radius to the conducting rim, and from there the circuit completes through the lower brush and the axle supporting the disc. This device generates an emf and a current, although the shape of the "circuit" is constant and thus the flux through the circuit does

3570:{\displaystyle \mathrm {d} \Phi _{B}=\int \mathbf {B} \cdot \mathrm {d} \mathbf {A} _{\text{sweep}}=\int \mathbf {B} \cdot (\mathbf {v} _{\mathbf {l} }\mathrm {d} t\times \mathrm {d} \mathbf {l} )=-\int \mathrm {d} t\,\mathrm {d} \mathbf {l} \cdot (\mathbf {v} _{\mathbf {l} }\times \mathbf {B} )} 3033:

is any given fixed time. We will show that the first term on the right-hand side corresponds to transformer emf, the second to motional emf (from the magnetic Lorentz force on charge carriers due to the motion or deformation of the conducting loop in the magnetic field). The first term on the

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This statement, however, is not always true and the reason is not just from the obvious reason that emf is undefined in empty space when no conductor is present. As noted in the previous section, Faraday's law is not guaranteed to work unless the velocity of the abstract curve

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It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor.

2479:{\displaystyle \mathbf {E} _{s}(\mathbf {r} ,t)\approx -{\frac {1}{4\pi }}\iiint _{V}\ {\frac {\left({\frac {\partial \mathbf {B} (\mathbf {r} ',t)}{\partial t}}\right)\times \left(\mathbf {r} -\mathbf {r} '\right)}{|\mathbf {r} -\mathbf {r} '|^{3}}}d^{3}\mathbf {r'} } 4524: 2126: 5115: 6043:

Examples of this sort, together with unsuccessful attempts to discover any motion of the earth relative to the "light medium," suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest.

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The proof of this is a little more difficult than the first term; more details and alternate approaches for the proof can be found in the references. As the loop moves and/or deforms, it sweeps out a surface (see the right figure). As a small part of the loop

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are along the same direction. Now we can see that, for the conductive loop, emf is same to the time-derivative of the magnetic flux through the loop except for the sign on it. Therefore, we now reach the equation of Faraday's law (for the conductive loop) as

2648: 2515: 4290:{\displaystyle \left.{\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}\right|_{t=t_{0}}=-\oint _{\partial \Sigma (t_{0})}{\bigl (}\mathbf {E} (t_{0})+\mathbf {v} _{\mathbf {l} }(t_{0})\times \mathbf {B} (t_{0}){\bigr )}\cdot \mathrm {d} \mathbf {l} .} 5158: 3772:{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\int _{\Sigma (t)}\mathbf {B} (t_{0})\cdot \mathrm {d} \mathbf {A} =-\oint _{\partial \Sigma (t_{0})}(\mathbf {v} _{\mathbf {l} }(t_{0})\times \mathbf {B} (t_{0}))\cdot \mathrm {d} \mathbf {l} } 1849: 1443:

Faraday's law contains the information about the relationships between both the magnitudes and the directions of its variables. However, the relationships between the directions are not explicit; they are hidden in the mathematical formula.

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Faraday's law had been discovered and one aspect of it (transformer emf) was formulated as the Maxwell–Faraday equation later. The equation of Faraday's law can be derived by the Maxwell–Faraday equation (describing transformer emf) and the

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Within two months, Faraday had found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady

6462: 1639: 1383: 1302:, defined as the energy available from a unit charge that has traveled once around the wire loop. (Although some sources state the definition differently, this expression was chosen for compatibility with the equations of 5041: 1448: 5634:

So the "flux rule" that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit applies whether the flux changes because the field changes or because the circuit moves (or both) ...

3201:{\displaystyle \int _{\Sigma (t_{0})}\left.{\frac {\partial \mathbf {B} }{\partial t}}\right|_{t=t_{0}}\cdot \mathrm {d} \mathbf {A} =-\oint _{\partial \Sigma (t_{0})}\mathbf {E} (t_{0})\cdot \mathrm {d} \mathbf {l} } 1030:, who in 1861–62 used Faraday's ideas as the basis of his quantitative electromagnetic theory. In Maxwell's papers, the time-varying aspect of electromagnetic induction is expressed as a differential equation which 7008:

This example of Faraday's Law makes it very clear that in the case of extended bodies care must be taken that the boundary used to determine the flux must not be stationary but must be moving with respect to the

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Alternating electric current flows through the solenoid on the left, producing a changing magnetic field. This field causes, by electromagnetic induction, an electric current to flow in the wire loop on the

3213: 115:(describing motional emf). The integral form of the Maxwell–Faraday equation describes only the transformer emf, while the equation of Faraday's law describes both the transformer emf and the motional emf. 5153: 6489:"71 years earlier, this scientist beat Einstein to relativity - Michael Faraday's 1834 law of induction was the key experiment behind the eventual discovery of relativity. Einstein admitted it himself" 5823: 3393:(note that this vector is toward out from the display in the right figure). Therefore, the change of the magnetic flux through the loop due to the deformation or movement of the loop over the time 4896: 989:

that occurred when the battery was connected and disconnected. His notebook entry also noted that fewer wraps for the battery side resulted in a greater disturbance of the galvanometer's needle.

4419:{\displaystyle {\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}=-\oint _{\partial \Sigma }\left(\mathbf {E} +\mathbf {v} _{\mathbf {l} }\times \mathbf {B} \right)\cdot \mathrm {d} \mathbf {l} .} 5046: 5913:

in K’ is considered as a result of the induction effect in the moving circuit, regardless of whether the charges are present in the circuit or not. In the conducting circuit, the field

2630:(by definition). This total time derivative can be evaluated and simplified with the help of the Maxwell–Faraday equation and some vector identities; the details are in the box below: 1056:

in 1834, describes "flux through the circuit", and gives the direction of the induced emf and current resulting from electromagnetic induction (elaborated upon in the examples below).

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A wire (solid red lines) connects to two touching metal plates (silver) to form a circuit. The whole system sits in a uniform magnetic field, normal to the page. If the abstract path

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In the case of a conductive loop, emf (Electromotive Force) is the electromagnetic work done on a unit charge when it has traveled around the loop once, and this work is done by the

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follows the primary path of current flow (marked in red), then the magnetic flux through this path changes dramatically as the plates are rotated, yet the emf is almost zero. After

2220:{\displaystyle \oint _{\partial \Sigma }\mathbf {E} \cdot \mathrm {d} \mathbf {l} =-{\frac {\mathrm {d} }{\mathrm {d} t}}\int _{\Sigma }\mathbf {B} \cdot \mathrm {d} \mathbf {A} .} 1492:

It is possible to find out the direction of the electromotive force (emf) directly from Faraday’s law, without invoking Lenz's law. A left hand rule helps doing that, as follows:

1162: 5253:{\textstyle \oint \left(\mathbf {v} \times \mathbf {B} \right)\cdot \mathrm {d} \mathbf {l} =\oint \left(\mathbf {v} _{l}\times \mathbf {B} \right)\cdot \mathrm {d} \mathbf {l} } 6670: 6036:

there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated.

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Faraday's notebook on August 29, 1831 describes an experimental demonstration of electromagnetic induction (see figure) that wraps two wires around opposite sides of an iron

5957: 4548: 1938:{\displaystyle \oint _{\partial \Sigma }\mathbf {E} \cdot \mathrm {d} \mathbf {l} =-\int _{\Sigma }{\frac {\partial \mathbf {B} }{\partial t}}\cdot \mathrm {d} \mathbf {A} } 1407: 5847:

is the vector potential. If the circuit area is changing in case of the constant magnetic field, then some part of the circuit is inevitably moving, and the electric field

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matches the actual velocity of the material conducting the electricity. The two examples illustrated below show that one often obtains incorrect results when the motion of

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moves with the same velocity as the material. Alternatively, one can always correctly calculate the emf by combining Lorentz force law with the Maxwell–Faraday equation:

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Faraday's Law, which states that the electromotive force around a closed path is equal to the negative of the time rate of change of magnetic flux enclosed by the path.

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suggested that when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. Indeed, a

1580: 1324: 4985: 2754:{\displaystyle {\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}={\frac {\mathrm {d} }{\mathrm {d} t}}\int _{\Sigma (t)}\mathbf {B} (t)\cdot \mathrm {d} \mathbf {A} } 2621:{\displaystyle {\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}={\frac {\mathrm {d} }{\mathrm {d} t}}\int _{\Sigma (t)}\mathbf {B} (t)\cdot \mathrm {d} \mathbf {A} } 5701: 6201: 1116:

of magnitude equal to the area of the element and with direction normal to the element and pointing "outward" (with respect to the orientation of the surface).

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Consider the time-derivative of magnetic flux through a closed boundary (loop) that can move or be deformed. The area bounded by the loop is denoted as

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We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of

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The integral can change over time for two reasons: The integrand can change, or the integration region can change. These add linearly, therefore:

1026:. However, scientists at the time widely rejected his theoretical ideas, mainly because they were not formulated mathematically. An exception was 33:), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil ( 1695:

The Maxwell–Faraday equation states that a time-varying magnetic field always accompanies a spatially varying (also possibly time-varying), non-

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is defined by the right-hand rule as one that points with the fingers of the right hand when the thumb points in the direction of the normal

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is negative, the direction of the electromotive force is opposite to the direction of the curved fingers (opposite to the yellow arrowheads).

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and (2) in general, the partial derivative with respect to time cannot be moved outside the integral since the area is a function of time."

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emerges in this part of the circuit in the comoving reference frame K’ as a result of the Lorentz transformation of the magnetic field

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is for the motional emf (due to the magnetic Lorentz force on charges by the motion or deformation of the loop in the magnetic field).

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two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.

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changes, or because the wire loop is moved or deformed, or both—Faraday's law of induction says that the wire loop acquires an

532: 5786: 6861: 6322: 6211: 6149: 547: 542: 169: 5627:. In the latter half of Part II of that paper, Maxwell gives a separate physical explanation for each of the two phenomena. 4519:{\displaystyle {\mathcal {E}}=\oint \left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)\cdot \mathrm {d} \mathbf {l} } 981:'s needle measured a transient current (which he called a "wave of electricity") on the right side's wire when he connected 7430: 5630:

A reference to these two aspects of electromagnetic induction is made in some modern textbooks. As Richard Feynman states:

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referred to as Faraday's law even though it is different from the original version of Faraday's law, and does not describe

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where "it is very important to notice that (1) is the velocity of the conductor ... not the velocity of the path element

5589: 5110:{\textstyle {\mathcal {E}}=\oint \left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)\cdot \mathrm {d} \mathbf {l} } 3292:{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\int _{\Sigma (t)}\mathbf {B} (t_{0})\cdot \mathrm {d} \mathbf {A} } 7369: 7223: 7098: 6968: 6896: 6805: 6653: 6626: 6553: 159: 427: 7493: 7436: 7394: 7547: 5678: 342: 921: 687: 164: 37:), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer ( 6488: 5604: 4957: 4901: 4612: 2497:(including the Maxwell–Faraday equation), along with Lorentz force law, are a sufficient foundation to derive 7463: 7309: 6560:

The magnetic flux is that flux which passes through any and every surface whose perimeter is the closed path.

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Davison, M. E. (1973). "A Simple Proof that the Lorentz Force, Law Implied Faraday's Law of Induction, when

5962: 6386: 6227: 5891:, present in the stationary reference frame K, which passes through the circuit. The presence of the field 1075: 567: 307: 174: 7409: 5288:

is any arbitrary closed loop in space whatsoever, then the total time derivative of magnetic flux through

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causes motion of the charges. In the reference frame K, it looks like appearance of emf of the induction

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is positive, the direction of the emf is the same as that of the curved fingers (yellow arrowheads). If

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The electromotive force around a closed path is equal to the negative of the time rate of change of the

6402:"Ueber die Bestimmung der Richtung der durch elektodynamische Vertheilung erregten galvanischen Ströme" 5623: 2502: 1832: 360: 4928: 7498: 7384: 2076:

is different from the behavior of the electric field generated by static charges. A charge-generated

2017: 1840: 1696: 914: 875: 402: 392: 332: 327: 267: 73: 5938: 4529: 1544:, is positive, the curved fingers show the direction of the electromotive force (yellow arrowheads). 1388: 7542: 7537: 7516: 7453: 7302: 412: 6822: 5992: 5916: 5894: 5872: 5850: 5828: 5764: 845: 347: 5638:

Yet in our explanation of the rule we have used two completely distinct laws for the two cases –

2253: 1285:. In more visual terms, the magnetic flux through the wire loop is proportional to the number of 725: 252: 242: 237: 7090: 7084: 6618: 6612: 850: 820: 7044: 6545: 6539: 6294: 6079: 5761:, that occurs in the circuit when the magnetic flux changes. In this case, the contribution to 2494: 1828: 1447: 1043: 672: 442: 217: 104: 7189: 6958: 6643: 6263: 7116: 6312: 6165: 2087: 2067: 1232:{\displaystyle \Phi _{B}=\iint _{\Sigma (t)}\mathbf {B} (t)\cdot \mathrm {d} \mathbf {A} \,,} 1137: 770: 457: 447: 397: 387: 5754:{\textstyle \mathbf {E} =-\nabla {\mathcal {E}}-{\frac {\partial \mathbf {A} }{\partial t}}} 7151: 6928: 6736: 6685: 6413: 4565:

consists of two components in average; one is the velocity of the charge along the segment

1306:.) Equivalently, it is the voltage that would be measured by cutting the wire to create an 970: 895: 795: 760: 512: 377: 277: 262: 197: 89: 3034:

right-hand side can be rewritten using the integral form of the Maxwell–Faraday equation:

134: 8: 7209: 7053: 7039: 6988:(5th ed.). Berlin: VEB Deutscher Verlag der Wissenschaften. eq. 20, p. 47. 6727: 5618: 5324: 5275: 1437: 1410: 1299: 1144: 1027: 1013: 998: 997:) current by rotating a copper disk near the bar magnet with a sliding electrical lead (" 855: 835: 830: 637: 622: 507: 477: 372: 302: 69: 7276: 7213: 7155: 6932: 6740: 6689: 6417: 2256:

of the overall electric field, can be approximated in the non-relativistic limit by the

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disconnected the left side's wire to a battery. This induction was due to the change in

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to that surface patch, the magnitude is the area of an infinitesimal patch of surface.

1770: 1751:{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}} 1303: 1064: 1009: 730: 470: 272: 232: 552: 7478: 7219: 7171: 7094: 7069: 6964: 6892: 6867: 6857: 6801: 6722: 6649: 6622: 6549: 6354: 6318: 6256: 6207: 6169: 6145: 4449: 790: 7130:"On the Covariant Representation of Integral Equations of the Electromagnetic Field" 2505:. Therefore, it is possible to "prove" Faraday's law starting with these equations. 1470:, and the normal n to that area, as represented by the fingers of the left hand. If 1460:, the change in flux, is found based on the relationship between the magnetic field 7468: 7458: 7404: 7354: 7159: 7057: 6936: 6744: 6693: 6421: 2228: 2091: 1436:

The laws of induction of electric currents in mathematical form was established by

1307: 1156: 1031: 890: 805: 765: 755: 642: 597: 580: 497: 432: 202: 126: 65: 57: 6584: 6453:"Relativity Wasn't Einstein's Miracle; It Was Waiting In Plain Sight For 71 Years" 6115: 5611:

generated by an electric force due to a changing magnetic field (described by the

1517:, the change in flux. Determine the initial and final fluxes (whose difference is 7379: 7374: 7325: 7185: 6139: 6094: 6089: 6049: 6020: 5269: 2257: 2013: 1773: 1688: 1318: 1060: 1019: 947: 825: 750: 745: 612: 487: 452: 312: 212: 25:

Faraday's experiment showing induction between coils of wire: The liquid battery

1101: 865: 7473: 7344: 5337:(which direction is along the disk surface normal). The magnetic Lorentz force 3579: 2508:

The starting point is the time-derivative of flux through an arbitrary surface

1811: 1792: 1634:{\displaystyle {\mathcal {E}}=-N{\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}} 1378:{\displaystyle {\mathcal {E}}=-{\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}},} 1121: 1023: 994: 974: 785: 780: 602: 492: 417: 367: 317: 290: 247: 222: 192: 185: 85: 61: 53: 7061: 6753: 6019:

Reflection on this apparent dichotomy was one of the principal paths that led

5036:{\displaystyle {\frac {\mathrm {d} \Phi _{B}}{\mathrm {d} t}}=-{\mathcal {E}}} 7531: 7414: 7289: 6871: 6697: 6425: 6375:. Vol. 2 (3rd ed.). Oxford University Press. pp. 178–179, 189. 6144:(4th ed.). New York & Oxford: Oxford University Press. p. 386. 2232: 2056: 1969: 1430: 1423: 1125: 1089: 1049: 986: 900: 885: 870: 810: 522: 437: 422: 337: 322: 227: 112: 7389: 7349: 6484: 6448: 6069: 5599:

Faraday's law is a single equation describing two different phenomena: the

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does not contribute to the work done on the charge since the direction of

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in 1832. Faraday was the first to publish the results of his experiments.

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Notes from Physics and Astronomy HyperPhysics at Georgia State University

5331:, sweeping the conducting radius circularly in the static magnetic field 1275: 1247: 1004: 957: 800: 652: 482: 144: 77: 6074: 1992: 1286: 517: 21: 6940: 6748: 5155:

is for the transformer emf (due to a time-varying magnetic field) and

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Align the curved fingers of the left hand with the loop (yellow line).

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into small surface elements. Each element is associated with a vector

7218:. Oxford: Clarendon Press. ch. III, sec. 530, p. 178. 7117:

The Feynman Lectures on Physics Vol. II Ch. 17: The Laws of Induction

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Magnetism and Electricity: A manual for students in advanced classes

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The electric vector field induced by a changing magnetic flux, the

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Stretch your thumb. The stretched thumb indicates the direction of

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The definition of surface integral relies on splitting the surface

592: 587: 207: 93: 81: 7294: 6120:. London and New York: Longmans, Green, & Co. Fig. 248, p. 245 5688: 1067:

theory was presented by this law of induction by Faraday in 1834.

1042:) is the form recognized today in the group of equations known as 6314:

The philosopher's tree: a selection of Michael Faraday's writings

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One can analyze examples like these by taking care that the path

562: 7089:(3rd ed.). Upper Saddle River, NJ: Prentice Hall. pp. 6617:(3rd ed.). Upper Saddle River, NJ: Prentice Hall. pp. 1699:

electric field, and vice versa. The Maxwell–Faraday equation is

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is negative, the direction of the emf is against the arrowheads.

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from the change in the magnetic field is made through the term

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is the given loop. Since the wire loop may be moving, we write

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explained electromagnetic induction using a concept he called

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In a macroscopic view, for charges on a segment of the loop,

966: 6767:"Bypassing Lenz's Rule - A Left Hand Rule for Faraday's Law" 6513: 4088: 3809: 3069: 2864: 2772: 7255:

A simple interactive tutorial on electromagnetic induction

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at the right-hand side is the explicit expression for the

1831:, and therefore plays a fundamental role in the theory of 1668:

An illustration of the Kelvin–Stokes theorem with surface

946:

Electromagnetic induction was discovered independently by

5818:{\textstyle -{\frac {\partial \mathbf {A} }{\partial t}}} 3210:

Next, we analyze the second term on the right-hand side:

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generated by a magnetic force on a moving wire (see the

2123:

is not changing in time, the equation can be rewritten:

6671:"Allgemeine Gesetze der inducirten elektrischen Ströme" 5989:, taken along the circuit, seems to generate the field 1317:

Faraday's law states that the emf is also given by the

29:

provides a current which flows through the small coil (

5789: 5704: 5161: 5123: 5049: 1814:. These fields can generally be functions of position 5995: 5965: 5941: 5919: 5897: 5875: 5853: 5831: 5767: 5385: 5280:

It is tempting to generalize Faraday's law to state:

4988: 4960: 4931: 4904: 4891:{\displaystyle (\mathbf {v} _{t}\times \mathbf {B} )} 4861: 4642: 4615: 4532: 4458: 4309: 4085: 3806: 3588: 3406: 3216: 3040: 2769: 2651: 2518: 2266: 2129: 1852: 1708: 1583: 1505:(brown), the normal to the area enclosed by the loop. 1429:

The direction of the electromotive force is given by

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The most widespread version of Faraday's law states:

7489:

Institute of Physics Michael Faraday Medal and Prize

6206:(5th ed.). Pearson:Prentice Hall. p. 255. 2012:

have a sign ambiguity; to get the correct sign, the

973:). His assessment of newly-discovered properties of 6856:. 4 (Fourth ed.). Cambridge University Press. 6431:A partial translation of the paper is available in 6353: 6255: 6003: 5981: 5951: 5927: 5905: 5883: 5861: 5839: 5817: 5775: 5753: 5562: 5252: 5147: 5109: 5035: 4973: 4946: 4917: 4890: 4847: 4628: 4542: 4518: 4418: 4289: 4072: 3771: 3569: 3291: 3200: 3016: 2753: 2620: 2478: 2219: 1937: 1750: 1633: 1401: 1377: 1231: 6437:. Cambridge, MA: Harvard Press. pp. 511–513. 7529: 7215:A treatise on electricity and magnetism, Vol. II 6389:. The Institution of Engineering and Technology. 6282:"Faraday's notebooks: Electromagnetic Induction" 2644:), then the time-derivative can be expressed as 1827:The Maxwell–Faraday equation is one of the four 1451:A Left Hand Rule for Faraday's Law. The sign of 6891:. Mineola, NY: Dover Publications. p. 56. 5689:Explanation based on four-dimensional formalism 5583: 4576:, and the other is the velocity of the segment 7019: 7017: 6795: 6232:Member Directory, National Academy of Sciences 5621:drew attention to this fact in his 1861 paper 1985:is an infinitesimal vector element of surface 1063:, much of the groundwork and discovery of his 7484:Royal Society of London Michael Faraday Prize 7310: 7268:– Highly animated lecture, with sound effects 7208: 7107:statement is about the "universal flux rule". 7038: 6960:Basic Theoretical Physics: A Concise Overview 6606: 6604: 6519: 6441: 6370: 6304: 5612: 5311:is divorced from the motion of the material. 4266: 4181: 4047: 3986: 2082:-field can be expressed as the gradient of a 1039: 922: 6845: 6843: 6524:(2nd ed.). Prentice-Hall. p. 100. 1654:is the magnetic flux through a single loop. 76:, is the fundamental operating principle of 7023: 7014: 6888:Introduction to electromagnetic engineering 6720: 6716: 6714: 6641: 6531: 6522:Electromagnetic Waves and Radiating Systems 6477: 6347: 6345: 6343: 6341: 6166:"Applications of electromagnetic induction" 4445:is the velocity of a part of the boundary. 1954:is a surface bounded by the closed contour 1657: 7317: 7303: 7076: 6997: 6995: 6910: 6908: 6884: 6878: 6601: 6578: 6576: 6574: 6572: 6570: 6568: 6520:Jordan, Edward; Balmain, Keith G. (1968). 6310: 6249: 6247: 2512:(that can be moved or deformed) in space: 1155:for the surface. The magnetic flux is the 929: 915: 133: 7190:"On the Electrodynamics of Moving Bodies" 7145: 7082: 6849: 6840: 6610: 6585:"The Feynman Lectures on Physics Vol. II" 3525: 1577:, Faraday's law of induction states that 1278:representing the element of flux through 1225: 1096: 7230:a treatise on electricity and magnetism. 6956: 6711: 6351: 6338: 6311:Faraday, Michael; Day, P. (1999-02-01). 6253: 6203:Fundamentals of applied electromagnetics 6131: 5693:In the general case, explanation of the 4974:{\displaystyle \mathrm {d} \mathbf {l} } 4918:{\displaystyle \mathrm {d} \mathbf {l} } 4629:{\displaystyle \mathrm {d} \mathbf {l} } 3366:, it sweeps out an area whose vector is 3300: 1663: 1446: 1100: 1074: 1003: 956: 20: 7266:Induction: Faraday's law and Lenz's law 7259:National High Magnetic Field Laboratory 7257:(click and drag magnet back and forth) 7134:Progress in Electromagnetics Research C 7127: 6992: 6983: 6952: 6950: 6914: 6905: 6796:Whelan, P. M.; Hodgeson, M. J. (1978). 6668: 6565: 6387:"Archives Biographies: Michael Faraday" 6373:A Treatise on Electricity and Magnetism 6279: 6244: 6055:On the Electrodynamics of Moving Bodies 5959:, the gradient of which in the form of 3305:The area swept out by a vector element 678:Electromagnetism and special relativity 7530: 7042:(1861). "On physical lines of force". 6483: 6447: 6290:The Royal Institution of Great Britain 6137: 6113: 5982:{\displaystyle -\nabla {\mathcal {E}}} 4430:is the boundary (loop) of the surface 3790:is the velocity of a part of the loop 1532:, as indicated by the stretched thumb. 7298: 7272:Electricity and Magnetism course page 6544:(5th ed.). McGraw-Hill. p. 6432: 6379: 6258:Physics: Principles with Applications 6199: 6184:"A Brief History of Electromagnetism" 5327:. The disc rotates with angular rate 2016:is used, as explained in the article 1843:, thereby reproducing Faraday's law: 698:Maxwell equations in curved spacetime 7431:Royal Institution Christmas Lectures 7184: 7024:Hughes, W. F.; Young, F. J. (1965). 6947: 6723:"A Left Hand Rule for Faraday's Law" 6645:Physics for Scientists and Engineers 6537: 6399: 6275: 6273: 3580:identities of triple scalar products 2090:, and has a zero path integral. See 1568:identical turns, each with the same 7324: 7026:The Electromagnetodynamics of Fluid 7004:Intermediate Electromagnetic Theory 7001: 6582: 5590:Moving magnet and conductor problem 3800:Putting these together results in, 2114:for which that path is a boundary. 1948:where, as indicated in the figure, 1645:is the number of turns of wire and 13: 7202: 6977: 6014: 5974: 5969: 5944: 5806: 5796: 5742: 5732: 5721: 5716: 5551: 5516: 5513: 5502: 5498: 5485: 5475: 5467: 5447: 5404: 5401: 5388: 5241: 5192: 5136: 5098: 5052: 5028: 5010: 4998: 4993: 4962: 4906: 4836: 4794: 4729: 4666: 4617: 4535: 4507: 4461: 4452:. Therefore, emf is expressed as 4404: 4355: 4352: 4331: 4319: 4314: 4275: 4158: 4155: 4111: 4099: 4094: 4056: 3963: 3960: 3930: 3884: 3881: 3832: 3820: 3815: 3760: 3675: 3672: 3652: 3613: 3598: 3592: 3527: 3518: 3496: 3485: 3437: 3413: 3408: 3280: 3241: 3226: 3220: 3189: 3143: 3140: 3120: 3084: 3074: 3046: 3000: 2961: 2946: 2940: 2915: 2879: 2869: 2841: 2795: 2783: 2778: 2742: 2710: 2695: 2689: 2673: 2661: 2656: 2609: 2577: 2562: 2556: 2540: 2528: 2523: 2372: 2340: 2205: 2191: 2176: 2170: 2152: 2138: 2135: 2097:The integral equation is true for 1926: 1913: 1903: 1895: 1875: 1861: 1858: 1739: 1729: 1709: 1621: 1609: 1604: 1586: 1394: 1362: 1350: 1345: 1330: 1216: 1184: 1167: 1035: 14: 7559: 7290:A free simulation on motional emf 7236: 7028:. John Wiley. Eq. (2.6–13) p. 53. 6501:from the original on 28 June 2023 6270: 4587:(the loop is deformed or moved). 72:(emf). This phenomenon, known as 7512: 7511: 7494:Faraday Medal (electrochemistry) 7437:The Chemical History of a Candle 7242: 6820: 6764: 6465:from the original on 3 July 2023 5997: 5921: 5899: 5877: 5855: 5833: 5800: 5769: 5736: 5706: 5594: 5556: 5540: 5526: 5479: 5452: 5436: 5422: 5413: 5353: 5316: 5246: 5228: 5214: 5197: 5179: 5171: 5141: 5128: 5103: 5085: 5077: 5069: 4967: 4947:{\displaystyle \mathbf {v} _{t}} 4934: 4911: 4881: 4867: 4841: 4825: 4811: 4799: 4783: 4769: 4760: 4746: 4734: 4718: 4701: 4686: 4671: 4655: 4647: 4622: 4512: 4494: 4486: 4478: 4409: 4391: 4381: 4375: 4366: 4280: 4244: 4218: 4212: 4187: 4061: 4025: 3999: 3993: 3935: 3906: 3765: 3733: 3707: 3701: 3657: 3628: 3560: 3550: 3544: 3532: 3501: 3478: 3472: 3460: 3443: 3429: 3326:when it has moved with velocity 3285: 3256: 3194: 3165: 3125: 3078: 3005: 2976: 2920: 2873: 2747: 2725: 2614: 2592: 2468: 2433: 2424: 2403: 2394: 2353: 2344: 2283: 2269: 2210: 2197: 2157: 2144: 1931: 1907: 1880: 1867: 1733: 1716: 1221: 1199: 1070: 7178: 7121: 7110: 7086:Introduction to Electrodynamics 7032: 6853:Introduction to Electrodynamics 6814: 6798:Essential Principles of Physics 6789: 6758: 6662: 6635: 6614:Introduction to Electrodynamics 6393: 6364: 6280:Faraday, Michael (1831-08-29). 6114:Poyser, Arthur William (1892). 5679:The Feynman Lectures on Physics 5117:. With breaking this integral, 2108:through space, and any surface 1835:. It can also be written in an 7370:Faraday's laws of electrolysis 6220: 6193: 6176: 6158: 6107: 5952:{\displaystyle {\mathcal {E}}} 5544: 5521: 5440: 5409: 4885: 4862: 4829: 4806: 4787: 4741: 4722: 4711: 4681: 4678: 4659: 4643: 4543:{\displaystyle {\mathcal {E}}} 4261: 4248: 4237: 4224: 4204: 4191: 4174: 4161: 4042: 4029: 4018: 4005: 3979: 3966: 3923: 3910: 3900: 3887: 3753: 3750: 3737: 3726: 3713: 3696: 3691: 3678: 3645: 3632: 3622: 3616: 3564: 3539: 3505: 3467: 3273: 3260: 3250: 3244: 3182: 3169: 3159: 3146: 3062: 3049: 2993: 2980: 2970: 2964: 2857: 2844: 2735: 2729: 2719: 2713: 2602: 2596: 2586: 2580: 2443: 2419: 2367: 2348: 2293: 2279: 1972:vector element of the contour 1402:{\displaystyle {\mathcal {E}}} 1292:When the flux changes—because 1209: 1203: 1193: 1187: 1040:Maxwell–Faraday equation below 1: 7464:Faraday Building (Manchester) 7395:Faraday's ice pail experiment 6957:Krey; Owen (14 August 2007). 6885:Harrington, Roger F. (2003). 6800:(2nd ed.). John Murray. 6669:Neumann, Franz Ernst (1846). 6406:Annalen der Physik und Chemie 6371:Clerk Maxwell, James (1904). 6254:Giancoli, Douglas C. (1998). 6101: 5263: 4556:is the unit charge velocity. 1526:) with respect to the normal 703:Relativistic electromagnetism 16:Basic law of electromagnetism 7083:Griffiths, David J. (1999). 6850:Griffiths, David J. (2017). 6771:www.PhysicsForArchitects.com 6611:Griffiths, David J. (1999). 6541:Engineering Electromagnetics 6352:Williams, L. Pearce (1965). 6141:Elements of Electromagnetics 6004:{\displaystyle \mathbf {E} } 5928:{\displaystyle \mathbf {E} } 5906:{\displaystyle \mathbf {E} } 5884:{\displaystyle \mathbf {B} } 5862:{\displaystyle \mathbf {E} } 5840:{\displaystyle \mathbf {A} } 5776:{\displaystyle \mathbf {E} } 5584:Faraday's law and relativity 4609:is same to the direction of 1289:that pass through the loop. 961:Faraday's 1831 demonstration 7: 7128:Fedosin, Sergey G. (2019). 6986:Theoretische Elektrotechnik 6921:American Journal of Physics 6589:feynmanlectures.caltech.edu 6062: 5366:Feynman Lectures on Physics 2070:. A nonzero circulation of 1264:is the magnetic field, and 1038:. Heaviside's version (see 10: 7564: 7340:Faraday's law of induction 7249:Faraday's law of induction 6829:. Georgia State University 6648:. Macmillan. p. 795. 5624:On Physical Lines of Force 5587: 5273: 5267: 2503:classical electromagnetism 2026:, a positive path element 1833:classical electromagnetism 1008:Faraday's disk, the first 941: 428:Liénard–Wiechert potential 46:Faraday's law of induction 7507: 7499:Faraday Lectureship Prize 7446: 7423: 7385:Faraday-efficiency effect 7332: 7284:Introducing Faraday's law 7062:10.1080/14786431003659180 6963:. Springer. p. 155. 6317:. CRC Press. p. 71. 6262:(5th ed.). pp. 6138:Sadiku, M. N. O. (2007). 693:Mathematical descriptions 403:Electromagnetic radiation 393:Electromagnetic induction 333:Magnetic vector potential 328:Magnetic scalar potential 74:electromagnetic induction 7517:Category:Michael Faraday 7454:Michael Faraday Memorial 6698:10.1002/andp.18461430103 6435:A Source Book in Physics 6426:10.1002/andp.18341073103 6360:. New York, Basic Books. 5648:for "circuit moves" and 5613:Maxwell–Faraday equation 2488: 1658:Maxwell–Faraday equation 1120:For a loop of wire in a 101:Maxwell–Faraday equation 5669:two different phenomena 2020:. For a planar surface 1535:If the change in flux, 1466:, the area of the loop 243:Electrostatic induction 238:Electrostatic discharge 7282:Tankersley and Mosca: 7045:Philosophical Magazine 6919:is Time Independent". 6642:Tipler; Mosca (2004). 6538:Hayt, William (1989). 6200:Ulaby, Fawwaz (2007). 6060: 6005: 5983: 5953: 5929: 5907: 5885: 5863: 5841: 5819: 5777: 5755: 5684: 5564: 5294:equals the emf around 5254: 5149: 5111: 5037: 4975: 4948: 4919: 4892: 4849: 4630: 4544: 4520: 4420: 4291: 4074: 3773: 3571: 3338: 3293: 3202: 3018: 2755: 2622: 2480: 2221: 2086:that is a solution to 1939: 1752: 1692: 1635: 1489: 1403: 1379: 1321:of the magnetic flux: 1250:of the moving surface 1233: 1117: 1097:Mathematical statement 1094: 1081: 1016: 962: 673:Electromagnetic tensor 64:will interact with an 42: 7164:10.2528/PIERC19062902 6433:Magie, W. M. (1963). 6029: 6006: 5984: 5954: 5930: 5908: 5886: 5864: 5842: 5820: 5778: 5756: 5664:for "field changes". 5632: 5588:Further information: 5565: 5348:not change with time. 5255: 5150: 5112: 5038: 4976: 4949: 4920: 4893: 4850: 4631: 4545: 4521: 4421: 4292: 4075: 3774: 3582:are used. Therefore, 3572: 3304: 3294: 3203: 3019: 2756: 2623: 2481: 2222: 2018:Kelvin–Stokes theorem 1940: 1841:Kelvin–Stokes theorem 1753: 1667: 1636: 1450: 1404: 1380: 1234: 1104: 1092:enclosed by the path. 1086: 1078: 1007: 960: 666:Covariant formulation 458:Synchrotron radiation 398:Electromagnetic pulse 388:Electromagnetic field 24: 7251:at Wikimedia Commons 7210:Clerk Maxwell, James 7054:Taylor & Francis 7040:Clerk Maxwell, James 6984:Simonyi, K. (1973). 6721:Yehuda Salu (2014). 6583:Feynman, Richard P. 5993: 5963: 5939: 5917: 5895: 5873: 5851: 5829: 5787: 5765: 5702: 5676:Richard P. Feynman, 5383: 5159: 5121: 5047: 4986: 4958: 4929: 4902: 4898:is perpendicular to 4859: 4640: 4613: 4530: 4456: 4307: 4083: 3804: 3586: 3404: 3348:moves with velocity 3214: 3038: 2767: 2649: 2516: 2264: 2254:solenoidal component 2127: 1850: 1706: 1581: 1560:For a tightly wound 1389: 1325: 1287:magnetic field lines 1163: 971:toroidal transformer 708:Stress–energy tensor 633:Reluctance (complex) 378:Displacement current 84:, and many types of 7548:Maxwell's equations 7156:2019arXiv191111138F 7002:Stewart, Joseph V. 6933:1973AmJPh..41..713D 6741:2014PhTea..52...48S 6728:The Physics Teacher 6690:1846AnP...143...31N 6418:1834AnP...107..483L 6400:Lenz, Emil (1834). 6080:Maxwell's equations 5619:James Clerk Maxwell 5325:homopolar generator 2495:Maxwell's equations 1991:. Its direction is 1829:Maxwell's equations 1438:Franz Ernst Neumann 1411:electromotive force 1136:is defined for any 1044:Maxwell's equations 1028:James Clerk Maxwell 1014:homopolar generator 623:Magnetomotive force 508:Electromotive force 478:Alternating current 413:Jefimenko equations 373:Cyclotron radiation 105:Maxwell's equations 70:electromotive force 7400:Faraday efficiency 6678:Annalen der Physik 6025:special relativity 6001: 5979: 5949: 5925: 5903: 5881: 5859: 5837: 5815: 5773: 5751: 5560: 5250: 5145: 5107: 5033: 4971: 4944: 4915: 4888: 4845: 4636:. Mathematically, 4626: 4540: 4516: 4416: 4287: 4070: 3769: 3567: 3359:over a short time 3339: 3289: 3198: 3014: 2751: 2618: 2476: 2217: 2088:Poisson's equation 1935: 1748: 1693: 1681:, and orientation 1631: 1490: 1399: 1375: 1310:, and attaching a 1304:special relativity 1276:vector dot product 1229: 1118: 1082: 1065:special relativity 1017: 1010:electric generator 963: 471:Electrical network 308:Gauss magnetic law 273:Static electricity 233:Electric potential 103:(listed as one of 43: 7525: 7524: 7479:IET Faraday Medal 7247:Media related to 6941:10.1119/1.1987339 6863:978-1-108-42041-9 6754:Video Explanation 6749:10.1119/1.4849156 6707:on 12 March 2020. 6324:978-0-7503-0570-9 6213:978-0-13-241326-8 6170:Boston University 6151:978-0-19-530048-2 5813: 5749: 5492: 5018: 4339: 4301: 4300: 4119: 3840: 3606: 3450: 3234: 3091: 2954: 2886: 2803: 2703: 2681: 2570: 2548: 2454: 2379: 2329: 2315: 2184: 1920: 1746: 1629: 1508:Find the sign of 1370: 1246:is an element of 939: 938: 638:Reluctance (real) 608:Gyrator–capacitor 553:Resonant cavities 443:Maxwell equations 60:predicting how a 7555: 7515: 7514: 7469:Faraday (crater) 7459:Faraday Building 7405:Electrochemistry 7355:Faraday constant 7319: 7312: 7305: 7296: 7295: 7246: 7232: 7197: 7196: 7194: 7186:Einstein, Albert 7182: 7176: 7175: 7149: 7125: 7119: 7114: 7108: 7104: 7080: 7074: 7073: 7036: 7030: 7029: 7021: 7012: 7011: 6999: 6990: 6989: 6981: 6975: 6974: 6954: 6945: 6944: 6912: 6903: 6902: 6882: 6876: 6875: 6847: 6838: 6837: 6835: 6834: 6818: 6812: 6811: 6793: 6787: 6786: 6784: 6782: 6773:. Archived from 6762: 6756: 6752: 6718: 6709: 6708: 6706: 6700:. Archived from 6675: 6666: 6660: 6659: 6639: 6633: 6632: 6608: 6599: 6598: 6596: 6595: 6580: 6563: 6562: 6535: 6529: 6528: 6517: 6511: 6510: 6508: 6506: 6487:(28 June 2023). 6481: 6475: 6474: 6472: 6470: 6451:(1 March 2019). 6445: 6439: 6438: 6429: 6397: 6391: 6390: 6383: 6377: 6376: 6368: 6362: 6361: 6359: 6349: 6336: 6335: 6333: 6331: 6308: 6302: 6301: 6299: 6293:. Archived from 6286: 6277: 6268: 6267: 6261: 6251: 6242: 6241: 6239: 6238: 6224: 6218: 6217: 6197: 6191: 6190: 6188: 6180: 6174: 6173: 6162: 6156: 6155: 6135: 6129: 6128: 6126: 6125: 6111: 6058: 6010: 6008: 6007: 6002: 6000: 5988: 5986: 5985: 5980: 5978: 5977: 5958: 5956: 5955: 5950: 5948: 5947: 5934: 5932: 5931: 5926: 5924: 5912: 5910: 5909: 5904: 5902: 5890: 5888: 5887: 5882: 5880: 5868: 5866: 5865: 5860: 5858: 5846: 5844: 5843: 5838: 5836: 5824: 5822: 5821: 5816: 5814: 5812: 5804: 5803: 5794: 5782: 5780: 5779: 5774: 5772: 5760: 5758: 5757: 5752: 5750: 5748: 5740: 5739: 5730: 5725: 5724: 5709: 5682: 5663: 5647: 5579: 5569: 5567: 5566: 5561: 5559: 5554: 5543: 5535: 5534: 5529: 5520: 5519: 5501: 5493: 5491: 5483: 5482: 5473: 5471: 5470: 5455: 5450: 5439: 5431: 5430: 5425: 5416: 5408: 5407: 5392: 5391: 5375: 5363: 5357: 5346: 5336: 5330: 5320: 5310: 5306: 5298: 5292: 5286: 5276:Hering's_Paradox 5259: 5257: 5256: 5251: 5249: 5244: 5236: 5232: 5231: 5223: 5222: 5217: 5200: 5195: 5187: 5183: 5182: 5174: 5154: 5152: 5151: 5146: 5144: 5139: 5131: 5116: 5114: 5113: 5108: 5106: 5101: 5093: 5089: 5088: 5080: 5072: 5056: 5055: 5042: 5040: 5039: 5034: 5032: 5031: 5019: 5017: 5013: 5007: 5006: 5005: 4996: 4990: 4980: 4978: 4977: 4972: 4970: 4965: 4953: 4951: 4950: 4945: 4943: 4942: 4937: 4924: 4922: 4921: 4916: 4914: 4909: 4897: 4895: 4894: 4889: 4884: 4876: 4875: 4870: 4854: 4852: 4851: 4846: 4844: 4839: 4828: 4820: 4819: 4814: 4802: 4797: 4786: 4778: 4777: 4772: 4763: 4755: 4754: 4749: 4737: 4732: 4721: 4710: 4709: 4704: 4695: 4694: 4689: 4674: 4669: 4658: 4650: 4635: 4633: 4632: 4627: 4625: 4620: 4608: 4597: 4586: 4575: 4564: 4555: 4549: 4547: 4546: 4541: 4539: 4538: 4525: 4523: 4522: 4517: 4515: 4510: 4502: 4498: 4497: 4489: 4481: 4465: 4464: 4444: 4433: 4429: 4425: 4423: 4422: 4417: 4412: 4407: 4399: 4395: 4394: 4386: 4385: 4384: 4378: 4369: 4359: 4358: 4340: 4338: 4334: 4328: 4327: 4326: 4317: 4311: 4296: 4294: 4293: 4288: 4283: 4278: 4270: 4269: 4260: 4259: 4247: 4236: 4235: 4223: 4222: 4221: 4215: 4203: 4202: 4190: 4185: 4184: 4178: 4177: 4173: 4172: 4143: 4142: 4141: 4140: 4124: 4120: 4118: 4114: 4108: 4107: 4106: 4097: 4091: 4079: 4077: 4076: 4071: 4069: 4065: 4064: 4059: 4051: 4050: 4041: 4040: 4028: 4017: 4016: 4004: 4003: 4002: 3996: 3990: 3989: 3983: 3982: 3978: 3977: 3943: 3939: 3938: 3933: 3922: 3921: 3909: 3904: 3903: 3899: 3898: 3864: 3863: 3862: 3861: 3845: 3841: 3839: 3835: 3829: 3828: 3827: 3818: 3812: 3796: 3789: 3778: 3776: 3775: 3770: 3768: 3763: 3749: 3748: 3736: 3725: 3724: 3712: 3711: 3710: 3704: 3695: 3694: 3690: 3689: 3660: 3655: 3644: 3643: 3631: 3626: 3625: 3607: 3605: 3601: 3595: 3590: 3576: 3574: 3573: 3568: 3563: 3555: 3554: 3553: 3547: 3535: 3530: 3521: 3504: 3499: 3488: 3483: 3482: 3481: 3475: 3463: 3452: 3451: 3448: 3446: 3440: 3432: 3421: 3420: 3411: 3399: 3392: 3365: 3358: 3347: 3336: 3325: 3318: 3311: 3298: 3296: 3295: 3290: 3288: 3283: 3272: 3271: 3259: 3254: 3253: 3235: 3233: 3229: 3223: 3218: 3207: 3205: 3204: 3199: 3197: 3192: 3181: 3180: 3168: 3163: 3162: 3158: 3157: 3128: 3123: 3115: 3114: 3113: 3112: 3096: 3092: 3090: 3082: 3081: 3072: 3066: 3065: 3061: 3060: 3032: 3023: 3021: 3020: 3015: 3013: 3009: 3008: 3003: 2992: 2991: 2979: 2974: 2973: 2955: 2953: 2949: 2943: 2938: 2928: 2924: 2923: 2918: 2910: 2909: 2908: 2907: 2891: 2887: 2885: 2877: 2876: 2867: 2861: 2860: 2856: 2855: 2827: 2826: 2825: 2824: 2808: 2804: 2802: 2798: 2792: 2791: 2790: 2781: 2775: 2760: 2758: 2757: 2752: 2750: 2745: 2728: 2723: 2722: 2704: 2702: 2698: 2692: 2687: 2682: 2680: 2676: 2670: 2669: 2668: 2659: 2653: 2643: 2633: 2632: 2627: 2625: 2624: 2619: 2617: 2612: 2595: 2590: 2589: 2571: 2569: 2565: 2559: 2554: 2549: 2547: 2543: 2537: 2536: 2535: 2526: 2520: 2511: 2485: 2483: 2482: 2477: 2475: 2474: 2465: 2464: 2455: 2453: 2452: 2451: 2446: 2440: 2436: 2427: 2422: 2416: 2415: 2411: 2410: 2406: 2397: 2384: 2380: 2378: 2370: 2360: 2356: 2347: 2338: 2331: 2327: 2326: 2325: 2316: 2314: 2303: 2286: 2278: 2277: 2272: 2248: 2242: 2229:surface integral 2226: 2224: 2223: 2218: 2213: 2208: 2200: 2195: 2194: 2185: 2183: 2179: 2173: 2168: 2160: 2155: 2147: 2142: 2141: 2122: 2113: 2107: 2092:gradient theorem 2081: 2075: 2065: 2051: 2045: 2039: 2032: 2025: 2011: 2004: 1990: 1984: 1977: 1967: 1960: 1953: 1944: 1942: 1941: 1936: 1934: 1929: 1921: 1919: 1911: 1910: 1901: 1899: 1898: 1883: 1878: 1870: 1865: 1864: 1823: 1819: 1809: 1790: 1768: 1757: 1755: 1754: 1749: 1747: 1745: 1737: 1736: 1727: 1719: 1686: 1680: 1673: 1653: 1644: 1640: 1638: 1637: 1632: 1630: 1628: 1624: 1618: 1617: 1616: 1607: 1601: 1590: 1589: 1576: 1567: 1555: 1543: 1531: 1525: 1516: 1504: 1487: 1478: 1469: 1465: 1459: 1421: 1408: 1406: 1405: 1400: 1398: 1397: 1384: 1382: 1381: 1376: 1371: 1369: 1365: 1359: 1358: 1357: 1348: 1342: 1334: 1333: 1297: 1284: 1273: 1263: 1257: 1245: 1238: 1236: 1235: 1230: 1224: 1219: 1202: 1197: 1196: 1175: 1174: 1157:surface integral 1154: 1142: 1135: 1115: 1108: 1052:, formulated by 1032:Oliver Heaviside 931: 924: 917: 598:Electric machine 581:Magnetic circuit 543:Parallel circuit 533:Network analysis 498:Electric current 433:London equations 278:Triboelectricity 268:Potential energy 137: 127:Electromagnetism 118: 117: 66:electric circuit 58:electromagnetism 7563: 7562: 7558: 7557: 7556: 7554: 7553: 7552: 7543:Michael Faraday 7538:Electrodynamics 7528: 7527: 7526: 7521: 7503: 7442: 7419: 7380:Faraday rotator 7375:Faraday paradox 7328: 7326:Michael Faraday 7323: 7239: 7226: 7205: 7203:Further reading 7200: 7192: 7183: 7179: 7126: 7122: 7115: 7111: 7105: 7101: 7081: 7077: 7037: 7033: 7022: 7015: 7006:. p. 396. 7000: 6993: 6982: 6978: 6971: 6955: 6948: 6913: 6906: 6899: 6883: 6879: 6864: 6848: 6841: 6832: 6830: 6823:"Faraday's Law" 6819: 6815: 6808: 6794: 6790: 6780: 6778: 6763: 6759: 6719: 6712: 6704: 6673: 6667: 6663: 6656: 6640: 6636: 6629: 6609: 6602: 6593: 6591: 6581: 6566: 6556: 6536: 6532: 6518: 6514: 6504: 6502: 6482: 6478: 6468: 6466: 6446: 6442: 6430: 6412:(31): 483–494. 6398: 6394: 6385: 6384: 6380: 6369: 6365: 6356:Michael Faraday 6350: 6339: 6329: 6327: 6325: 6309: 6305: 6297: 6284: 6278: 6271: 6252: 6245: 6236: 6234: 6226: 6225: 6221: 6214: 6198: 6194: 6186: 6182: 6181: 6177: 6164: 6163: 6159: 6152: 6136: 6132: 6123: 6121: 6112: 6108: 6104: 6099: 6090:Faraday paradox 6065: 6059: 6050:Albert Einstein 6048: 6021:Albert Einstein 6017: 6015:Einstein's view 5996: 5994: 5991: 5990: 5973: 5972: 5964: 5961: 5960: 5943: 5942: 5940: 5937: 5936: 5920: 5918: 5915: 5914: 5898: 5896: 5893: 5892: 5876: 5874: 5871: 5870: 5854: 5852: 5849: 5848: 5832: 5830: 5827: 5826: 5805: 5799: 5795: 5793: 5788: 5785: 5784: 5768: 5766: 5763: 5762: 5741: 5735: 5731: 5729: 5720: 5719: 5705: 5703: 5700: 5699: 5691: 5683: 5675: 5659: 5649: 5639: 5609:transformer emf 5597: 5592: 5586: 5574: 5555: 5550: 5539: 5530: 5525: 5524: 5512: 5508: 5497: 5484: 5478: 5474: 5472: 5466: 5462: 5451: 5446: 5435: 5426: 5421: 5420: 5412: 5400: 5396: 5387: 5386: 5384: 5381: 5380: 5373: 5368: 5361: 5358: 5349: 5338: 5332: 5328: 5321: 5308: 5304: 5296: 5290: 5284: 5278: 5272: 5270:Faraday paradox 5266: 5245: 5240: 5227: 5218: 5213: 5212: 5211: 5207: 5196: 5191: 5178: 5170: 5169: 5165: 5160: 5157: 5156: 5140: 5135: 5127: 5122: 5119: 5118: 5102: 5097: 5084: 5076: 5068: 5067: 5063: 5051: 5050: 5048: 5045: 5044: 5027: 5026: 5009: 5008: 5001: 4997: 4992: 4991: 4989: 4987: 4984: 4983: 4966: 4961: 4959: 4956: 4955: 4938: 4933: 4932: 4930: 4927: 4926: 4910: 4905: 4903: 4900: 4899: 4880: 4871: 4866: 4865: 4860: 4857: 4856: 4840: 4835: 4824: 4815: 4810: 4809: 4798: 4793: 4782: 4773: 4768: 4767: 4759: 4750: 4745: 4744: 4733: 4728: 4717: 4705: 4700: 4699: 4690: 4685: 4684: 4670: 4665: 4654: 4646: 4641: 4638: 4637: 4621: 4616: 4614: 4611: 4610: 4607: 4599: 4596: 4588: 4585: 4577: 4574: 4566: 4560: 4551: 4534: 4533: 4531: 4528: 4527: 4511: 4506: 4493: 4485: 4477: 4476: 4472: 4460: 4459: 4457: 4454: 4453: 4443: 4435: 4431: 4427: 4408: 4403: 4390: 4380: 4379: 4374: 4373: 4365: 4364: 4360: 4351: 4347: 4330: 4329: 4322: 4318: 4313: 4312: 4310: 4308: 4305: 4304: 4303:The result is: 4279: 4274: 4265: 4264: 4255: 4251: 4243: 4231: 4227: 4217: 4216: 4211: 4210: 4198: 4194: 4186: 4180: 4179: 4168: 4164: 4154: 4150: 4136: 4132: 4125: 4110: 4109: 4102: 4098: 4093: 4092: 4090: 4087: 4086: 4084: 4081: 4080: 4060: 4055: 4046: 4045: 4036: 4032: 4024: 4012: 4008: 3998: 3997: 3992: 3991: 3985: 3984: 3973: 3969: 3959: 3955: 3951: 3947: 3934: 3929: 3917: 3913: 3905: 3894: 3890: 3880: 3876: 3872: 3868: 3857: 3853: 3846: 3831: 3830: 3823: 3819: 3814: 3813: 3811: 3808: 3807: 3805: 3802: 3801: 3791: 3788: 3780: 3764: 3759: 3744: 3740: 3732: 3720: 3716: 3706: 3705: 3700: 3699: 3685: 3681: 3671: 3667: 3656: 3651: 3639: 3635: 3627: 3612: 3608: 3597: 3596: 3591: 3589: 3587: 3584: 3583: 3559: 3549: 3548: 3543: 3542: 3531: 3526: 3517: 3500: 3495: 3484: 3477: 3476: 3471: 3470: 3459: 3447: 3442: 3441: 3436: 3428: 3416: 3412: 3407: 3405: 3402: 3401: 3394: 3383: 3374: 3367: 3360: 3357: 3349: 3342: 3335: 3327: 3320: 3313: 3306: 3284: 3279: 3267: 3263: 3255: 3240: 3236: 3225: 3224: 3219: 3217: 3215: 3212: 3211: 3193: 3188: 3176: 3172: 3164: 3153: 3149: 3139: 3135: 3124: 3119: 3108: 3104: 3097: 3083: 3077: 3073: 3071: 3068: 3067: 3056: 3052: 3045: 3041: 3039: 3036: 3035: 3031: 3025: 3004: 2999: 2987: 2983: 2975: 2960: 2956: 2945: 2944: 2939: 2937: 2936: 2932: 2919: 2914: 2903: 2899: 2892: 2878: 2872: 2868: 2866: 2863: 2862: 2851: 2847: 2840: 2836: 2835: 2831: 2820: 2816: 2809: 2794: 2793: 2786: 2782: 2777: 2776: 2774: 2771: 2770: 2768: 2765: 2764: 2746: 2741: 2724: 2709: 2705: 2694: 2693: 2688: 2686: 2672: 2671: 2664: 2660: 2655: 2654: 2652: 2650: 2647: 2646: 2637: 2613: 2608: 2591: 2576: 2572: 2561: 2560: 2555: 2553: 2539: 2538: 2531: 2527: 2522: 2521: 2519: 2517: 2514: 2513: 2509: 2491: 2467: 2466: 2460: 2456: 2447: 2442: 2441: 2432: 2431: 2423: 2418: 2417: 2402: 2401: 2393: 2392: 2388: 2371: 2352: 2351: 2343: 2339: 2337: 2333: 2332: 2330: 2321: 2317: 2307: 2302: 2282: 2273: 2268: 2267: 2265: 2262: 2261: 2258:volume integral 2244: 2241: 2235: 2209: 2204: 2196: 2190: 2186: 2175: 2174: 2169: 2167: 2156: 2151: 2143: 2134: 2130: 2128: 2125: 2124: 2118: 2117:If the surface 2109: 2102: 2077: 2071: 2060: 2047: 2046:to the surface 2041: 2034: 2027: 2021: 2014:right-hand rule 2006: 1999: 1986: 1979: 1973: 1962: 1955: 1949: 1946: 1930: 1925: 1912: 1906: 1902: 1900: 1894: 1890: 1879: 1874: 1866: 1857: 1853: 1851: 1848: 1847: 1821: 1815: 1796: 1777: 1766: 1759: 1738: 1732: 1728: 1726: 1715: 1707: 1704: 1703: 1689:right-hand rule 1682: 1675: 1674:, its boundary 1669: 1660: 1652: 1646: 1642: 1620: 1619: 1612: 1608: 1603: 1602: 1600: 1585: 1584: 1582: 1579: 1578: 1575: 1569: 1565: 1554: 1548: 1542: 1536: 1527: 1524: 1518: 1515: 1509: 1500: 1486: 1480: 1477: 1471: 1467: 1461: 1458: 1452: 1420: 1414: 1393: 1392: 1390: 1387: 1386: 1361: 1360: 1353: 1349: 1344: 1343: 1341: 1329: 1328: 1326: 1323: 1322: 1293: 1279: 1265: 1259: 1251: 1240: 1220: 1215: 1198: 1183: 1179: 1170: 1166: 1164: 1161: 1160: 1148: 1140: 1134: 1128: 1110: 1106: 1099: 1073: 1061:Albert Einstein 1020:Michael Faraday 969:(like a modern 948:Michael Faraday 944: 935: 906: 905: 721: 713: 712: 668: 658: 657: 613:Induction motor 583: 573: 572: 488:Current density 473: 463: 462: 453:Poynting vector 363: 361:Electrodynamics 353: 352: 348:Right-hand rule 313:Magnetic dipole 303:Biot–Savart law 293: 283: 282: 218:Electric dipole 213:Electric charge 188: 86:electric motors 17: 12: 11: 5: 7561: 7551: 7550: 7545: 7540: 7523: 7522: 7520: 7519: 7508: 7505: 7504: 7502: 7501: 7496: 7491: 7486: 7481: 7476: 7474:Faraday Future 7471: 7466: 7461: 7456: 7450: 7448: 7444: 7443: 7441: 7440: 7433: 7427: 7425: 7421: 7420: 7418: 7417: 7412: 7407: 7402: 7397: 7392: 7387: 7382: 7377: 7372: 7367: 7362: 7357: 7352: 7347: 7345:Faraday effect 7342: 7336: 7334: 7330: 7329: 7322: 7321: 7314: 7307: 7299: 7293: 7292: 7287: 7279: 7274: 7264:Roberto Vega. 7261: 7252: 7238: 7237:External links 7235: 7234: 7233: 7224: 7204: 7201: 7199: 7198: 7177: 7120: 7109: 7099: 7075: 7031: 7013: 6991: 6976: 6969: 6946: 6904: 6897: 6877: 6862: 6839: 6821:Nave, Carl R. 6813: 6806: 6788: 6765:Salu, Yehuda. 6757: 6710: 6661: 6654: 6634: 6627: 6600: 6564: 6554: 6530: 6512: 6476: 6440: 6392: 6378: 6363: 6337: 6323: 6303: 6300:on 2021-08-30. 6269: 6243: 6228:"Joseph Henry" 6219: 6212: 6192: 6175: 6157: 6150: 6130: 6105: 6103: 6100: 6098: 6097: 6092: 6087: 6082: 6077: 6072: 6066: 6064: 6061: 6046: 6016: 6013: 5999: 5976: 5971: 5968: 5946: 5923: 5901: 5879: 5857: 5835: 5811: 5808: 5802: 5798: 5792: 5771: 5747: 5744: 5738: 5734: 5728: 5723: 5718: 5715: 5712: 5708: 5690: 5687: 5673: 5655: 5596: 5593: 5585: 5582: 5571: 5570: 5558: 5553: 5549: 5546: 5542: 5538: 5533: 5528: 5523: 5518: 5515: 5511: 5507: 5504: 5500: 5496: 5490: 5487: 5481: 5477: 5469: 5465: 5461: 5458: 5454: 5449: 5445: 5442: 5438: 5434: 5429: 5424: 5419: 5415: 5411: 5406: 5403: 5399: 5395: 5390: 5370: 5369: 5359: 5352: 5350: 5322: 5315: 5265: 5262: 5248: 5243: 5239: 5235: 5230: 5226: 5221: 5216: 5210: 5206: 5203: 5199: 5194: 5190: 5186: 5181: 5177: 5173: 5168: 5164: 5143: 5138: 5134: 5130: 5126: 5105: 5100: 5096: 5092: 5087: 5083: 5079: 5075: 5071: 5066: 5062: 5059: 5054: 5030: 5025: 5022: 5016: 5012: 5004: 5000: 4995: 4969: 4964: 4941: 4936: 4913: 4908: 4887: 4883: 4879: 4874: 4869: 4864: 4843: 4838: 4834: 4831: 4827: 4823: 4818: 4813: 4808: 4805: 4801: 4796: 4792: 4789: 4785: 4781: 4776: 4771: 4766: 4762: 4758: 4753: 4748: 4743: 4740: 4736: 4731: 4727: 4724: 4720: 4716: 4713: 4708: 4703: 4698: 4693: 4688: 4683: 4680: 4677: 4673: 4668: 4664: 4661: 4657: 4653: 4649: 4645: 4624: 4619: 4603: 4592: 4581: 4570: 4537: 4514: 4509: 4505: 4501: 4496: 4492: 4488: 4484: 4480: 4475: 4471: 4468: 4463: 4439: 4415: 4411: 4406: 4402: 4398: 4393: 4389: 4383: 4377: 4372: 4368: 4363: 4357: 4354: 4350: 4346: 4343: 4337: 4333: 4325: 4321: 4316: 4299: 4298: 4286: 4282: 4277: 4273: 4268: 4263: 4258: 4254: 4250: 4246: 4242: 4239: 4234: 4230: 4226: 4220: 4214: 4209: 4206: 4201: 4197: 4193: 4189: 4183: 4176: 4171: 4167: 4163: 4160: 4157: 4153: 4149: 4146: 4139: 4135: 4131: 4128: 4123: 4117: 4113: 4105: 4101: 4096: 4089: 4068: 4063: 4058: 4054: 4049: 4044: 4039: 4035: 4031: 4027: 4023: 4020: 4015: 4011: 4007: 4001: 3995: 3988: 3981: 3976: 3972: 3968: 3965: 3962: 3958: 3954: 3950: 3946: 3942: 3937: 3932: 3928: 3925: 3920: 3916: 3912: 3908: 3902: 3897: 3893: 3889: 3886: 3883: 3879: 3875: 3871: 3867: 3860: 3856: 3852: 3849: 3844: 3838: 3834: 3826: 3822: 3817: 3810: 3784: 3767: 3762: 3758: 3755: 3752: 3747: 3743: 3739: 3735: 3731: 3728: 3723: 3719: 3715: 3709: 3703: 3698: 3693: 3688: 3684: 3680: 3677: 3674: 3670: 3666: 3663: 3659: 3654: 3650: 3647: 3642: 3638: 3634: 3630: 3624: 3621: 3618: 3615: 3611: 3604: 3600: 3594: 3566: 3562: 3558: 3552: 3546: 3541: 3538: 3534: 3529: 3524: 3520: 3516: 3513: 3510: 3507: 3503: 3498: 3494: 3491: 3487: 3480: 3474: 3469: 3466: 3462: 3458: 3455: 3445: 3439: 3435: 3431: 3427: 3424: 3419: 3415: 3410: 3379: 3372: 3353: 3331: 3287: 3282: 3278: 3275: 3270: 3266: 3262: 3258: 3252: 3249: 3246: 3243: 3239: 3232: 3228: 3222: 3196: 3191: 3187: 3184: 3179: 3175: 3171: 3167: 3161: 3156: 3152: 3148: 3145: 3142: 3138: 3134: 3131: 3127: 3122: 3118: 3111: 3107: 3103: 3100: 3095: 3089: 3086: 3080: 3076: 3070: 3064: 3059: 3055: 3051: 3048: 3044: 3029: 3012: 3007: 3002: 2998: 2995: 2990: 2986: 2982: 2978: 2972: 2969: 2966: 2963: 2959: 2952: 2948: 2942: 2935: 2931: 2927: 2922: 2917: 2913: 2906: 2902: 2898: 2895: 2890: 2884: 2881: 2875: 2871: 2865: 2859: 2854: 2850: 2846: 2843: 2839: 2834: 2830: 2823: 2819: 2815: 2812: 2807: 2801: 2797: 2789: 2785: 2780: 2773: 2749: 2744: 2740: 2737: 2734: 2731: 2727: 2721: 2718: 2715: 2712: 2708: 2701: 2697: 2691: 2685: 2679: 2675: 2667: 2663: 2658: 2616: 2611: 2607: 2604: 2601: 2598: 2594: 2588: 2585: 2582: 2579: 2575: 2568: 2564: 2558: 2552: 2546: 2542: 2534: 2530: 2525: 2490: 2487: 2473: 2470: 2463: 2459: 2450: 2445: 2439: 2435: 2430: 2426: 2421: 2414: 2409: 2405: 2400: 2396: 2391: 2387: 2383: 2377: 2374: 2369: 2366: 2363: 2359: 2355: 2350: 2346: 2342: 2336: 2324: 2320: 2313: 2310: 2306: 2301: 2298: 2295: 2292: 2289: 2285: 2281: 2276: 2271: 2237: 2216: 2212: 2207: 2203: 2199: 2193: 2189: 2182: 2178: 2172: 2166: 2163: 2159: 2154: 2150: 2146: 2140: 2137: 2133: 1933: 1928: 1924: 1918: 1915: 1909: 1905: 1897: 1893: 1889: 1886: 1882: 1877: 1873: 1869: 1863: 1860: 1856: 1845: 1812:magnetic field 1793:electric field 1744: 1741: 1735: 1731: 1725: 1722: 1718: 1714: 1711: 1701: 1659: 1656: 1648: 1627: 1623: 1615: 1611: 1606: 1599: 1596: 1593: 1588: 1571: 1564:, composed of 1558: 1557: 1550: 1545: 1538: 1533: 1520: 1511: 1506: 1497: 1482: 1473: 1454: 1416: 1396: 1374: 1368: 1364: 1356: 1352: 1347: 1340: 1337: 1332: 1319:rate of change 1314:to the leads. 1228: 1223: 1218: 1214: 1211: 1208: 1205: 1201: 1195: 1192: 1189: 1186: 1182: 1178: 1173: 1169: 1130: 1122:magnetic field 1098: 1095: 1072: 1069: 1024:lines of force 999:Faraday's disk 975:electromagnets 943: 940: 937: 936: 934: 933: 926: 919: 911: 908: 907: 904: 903: 898: 893: 888: 883: 878: 873: 868: 863: 858: 853: 848: 843: 838: 833: 828: 823: 818: 813: 808: 803: 798: 793: 788: 783: 778: 773: 768: 763: 758: 753: 748: 743: 738: 733: 728: 722: 719: 718: 715: 714: 711: 710: 705: 700: 695: 690: 688:Four-potential 685: 680: 675: 669: 664: 663: 660: 659: 656: 655: 650: 645: 640: 635: 630: 625: 620: 615: 610: 605: 603:Electric motor 600: 595: 590: 584: 579: 578: 575: 574: 571: 570: 565: 560: 558:Series circuit 555: 550: 545: 540: 535: 530: 528:Kirchhoff laws 525: 520: 515: 510: 505: 500: 495: 493:Direct current 490: 485: 480: 474: 469: 468: 465: 464: 461: 460: 455: 450: 448:Maxwell tensor 445: 440: 435: 430: 425: 420: 418:Larmor formula 415: 410: 405: 400: 395: 390: 385: 380: 375: 370: 368:Bremsstrahlung 364: 359: 358: 355: 354: 351: 350: 345: 340: 335: 330: 325: 320: 318:Magnetic field 315: 310: 305: 300: 294: 291:Magnetostatics 289: 288: 285: 284: 281: 280: 275: 270: 265: 260: 255: 250: 245: 240: 235: 230: 225: 223:Electric field 220: 215: 210: 205: 200: 195: 193:Charge density 189: 186:Electrostatics 184: 183: 180: 179: 178: 177: 172: 167: 162: 157: 152: 147: 139: 138: 130: 129: 123: 122: 121:Articles about 68:to produce an 62:magnetic field 15: 9: 6: 4: 3: 2: 7560: 7549: 7546: 7544: 7541: 7539: 7536: 7535: 7533: 7518: 7510: 7509: 7506: 7500: 7497: 7495: 7492: 7490: 7487: 7485: 7482: 7480: 7477: 7475: 7472: 7470: 7467: 7465: 7462: 7460: 7457: 7455: 7452: 7451: 7449: 7445: 7439: 7438: 7434: 7432: 7429: 7428: 7426: 7422: 7416: 7415:Line of force 7413: 7411: 7408: 7406: 7403: 7401: 7398: 7396: 7393: 7391: 7388: 7386: 7383: 7381: 7378: 7376: 7373: 7371: 7368: 7366: 7363: 7361: 7358: 7356: 7353: 7351: 7348: 7346: 7343: 7341: 7338: 7337: 7335: 7331: 7327: 7320: 7315: 7313: 7308: 7306: 7301: 7300: 7297: 7291: 7288: 7286: 7285: 7280: 7278: 7275: 7273: 7269: 7267: 7262: 7260: 7256: 7253: 7250: 7245: 7241: 7240: 7231: 7227: 7225:0-486-60637-6 7221: 7217: 7216: 7211: 7207: 7206: 7191: 7187: 7181: 7173: 7169: 7165: 7161: 7157: 7153: 7148: 7143: 7139: 7135: 7131: 7124: 7118: 7113: 7102: 7100:0-13-805326-X 7096: 7092: 7088: 7087: 7079: 7071: 7067: 7063: 7059: 7055: 7051: 7047: 7046: 7041: 7035: 7027: 7020: 7018: 7010: 7005: 6998: 6996: 6987: 6980: 6972: 6970:9783540368052 6966: 6962: 6961: 6953: 6951: 6942: 6938: 6934: 6930: 6926: 6922: 6918: 6911: 6909: 6900: 6898:0-486-43241-6 6894: 6890: 6889: 6881: 6873: 6869: 6865: 6859: 6855: 6854: 6846: 6844: 6828: 6824: 6817: 6809: 6807:0-7195-3382-1 6803: 6799: 6792: 6777:on 7 May 2020 6776: 6772: 6768: 6761: 6755: 6750: 6746: 6742: 6738: 6734: 6730: 6729: 6724: 6717: 6715: 6703: 6699: 6695: 6691: 6687: 6683: 6679: 6672: 6665: 6657: 6655:9780716708100 6651: 6647: 6646: 6638: 6630: 6628:0-13-805326-X 6624: 6620: 6616: 6615: 6607: 6605: 6590: 6586: 6579: 6577: 6575: 6573: 6571: 6569: 6561: 6557: 6555:0-07-027406-1 6551: 6547: 6543: 6542: 6534: 6527: 6523: 6516: 6500: 6496: 6495: 6490: 6486: 6485:Siegel, Ethan 6480: 6464: 6460: 6459: 6454: 6450: 6449:Siegel, Ethan 6444: 6436: 6427: 6423: 6419: 6415: 6411: 6407: 6403: 6396: 6388: 6382: 6374: 6367: 6358: 6357: 6348: 6346: 6344: 6342: 6326: 6320: 6316: 6315: 6307: 6296: 6292: 6291: 6283: 6276: 6274: 6265: 6260: 6259: 6250: 6248: 6233: 6229: 6223: 6215: 6209: 6205: 6204: 6196: 6185: 6179: 6172:. 1999-07-22. 6171: 6167: 6161: 6153: 6147: 6143: 6142: 6134: 6119: 6118: 6110: 6106: 6096: 6093: 6091: 6088: 6086: 6083: 6081: 6078: 6076: 6073: 6071: 6068: 6067: 6057: 6056: 6051: 6045: 6041: 6037: 6033: 6028: 6026: 6022: 6012: 5966: 5809: 5790: 5745: 5726: 5713: 5710: 5696: 5686: 5681: 5680: 5672: 5670: 5665: 5662: 5658: 5653: 5646: 5642: 5636: 5631: 5628: 5626: 5625: 5620: 5616: 5614: 5610: 5606: 5605:Lorentz force 5602: 5595:Two phenomena 5591: 5581: 5578: 5547: 5536: 5531: 5509: 5505: 5494: 5488: 5463: 5459: 5456: 5443: 5432: 5427: 5417: 5397: 5393: 5379: 5378: 5377: 5367: 5356: 5351: 5345: 5341: 5335: 5326: 5319: 5314: 5313: 5312: 5301: 5295: 5289: 5283: 5277: 5271: 5261: 5237: 5233: 5224: 5219: 5208: 5204: 5201: 5188: 5184: 5175: 5166: 5162: 5132: 5124: 5094: 5090: 5081: 5073: 5064: 5060: 5057: 5023: 5020: 5014: 5002: 4939: 4877: 4872: 4832: 4821: 4816: 4803: 4790: 4779: 4774: 4764: 4756: 4751: 4738: 4725: 4714: 4706: 4696: 4691: 4675: 4662: 4651: 4606: 4602: 4595: 4591: 4584: 4580: 4573: 4569: 4563: 4557: 4554: 4503: 4499: 4490: 4482: 4473: 4469: 4466: 4451: 4450:Lorentz force 4446: 4442: 4438: 4413: 4400: 4396: 4387: 4370: 4361: 4348: 4344: 4341: 4335: 4323: 4297: 4284: 4271: 4256: 4252: 4240: 4232: 4228: 4207: 4199: 4195: 4169: 4165: 4151: 4147: 4144: 4137: 4133: 4129: 4126: 4121: 4115: 4103: 4066: 4052: 4037: 4033: 4021: 4013: 4009: 3974: 3970: 3956: 3952: 3948: 3944: 3940: 3926: 3918: 3914: 3895: 3891: 3877: 3873: 3869: 3865: 3858: 3854: 3850: 3847: 3842: 3836: 3824: 3798: 3795: 3787: 3783: 3756: 3745: 3741: 3729: 3721: 3717: 3686: 3682: 3668: 3664: 3661: 3648: 3640: 3636: 3619: 3609: 3602: 3581: 3556: 3536: 3522: 3514: 3511: 3508: 3492: 3489: 3464: 3456: 3453: 3433: 3425: 3422: 3417: 3398: 3391: 3387: 3382: 3378: 3371: 3364: 3356: 3352: 3346: 3334: 3330: 3324: 3317: 3310: 3303: 3299: 3276: 3268: 3264: 3247: 3237: 3230: 3208: 3185: 3177: 3173: 3154: 3150: 3136: 3132: 3129: 3116: 3109: 3105: 3101: 3098: 3093: 3087: 3057: 3053: 3042: 3028: 3010: 2996: 2988: 2984: 2967: 2957: 2950: 2933: 2929: 2925: 2911: 2904: 2900: 2896: 2893: 2888: 2882: 2852: 2848: 2837: 2832: 2828: 2821: 2817: 2813: 2810: 2805: 2799: 2787: 2761: 2738: 2732: 2716: 2706: 2699: 2683: 2677: 2665: 2641: 2635: 2634: 2631: 2628: 2605: 2599: 2583: 2573: 2566: 2550: 2544: 2532: 2506: 2504: 2500: 2496: 2486: 2471: 2461: 2457: 2448: 2437: 2428: 2412: 2407: 2398: 2389: 2385: 2381: 2375: 2364: 2361: 2357: 2334: 2322: 2318: 2311: 2308: 2304: 2299: 2296: 2290: 2287: 2274: 2259: 2255: 2250: 2247: 2240: 2234: 2233:magnetic flux 2230: 2214: 2201: 2187: 2180: 2164: 2161: 2148: 2131: 2121: 2115: 2112: 2106: 2100: 2095: 2093: 2089: 2085: 2080: 2074: 2069: 2064: 2058: 2057:line integral 2053: 2050: 2044: 2038: 2031: 2024: 2019: 2015: 2010: 2003: 1996: 1994: 1989: 1983: 1976: 1971: 1970:infinitesimal 1966: 1959: 1952: 1945: 1922: 1916: 1891: 1887: 1884: 1871: 1854: 1844: 1842: 1838: 1837:integral form 1834: 1830: 1825: 1818: 1813: 1807: 1803: 1799: 1794: 1788: 1784: 1780: 1775: 1772: 1764: 1758: 1742: 1723: 1720: 1712: 1700: 1698: 1690: 1685: 1679: 1672: 1666: 1662: 1655: 1651: 1625: 1613: 1597: 1594: 1591: 1574: 1563: 1553: 1546: 1541: 1534: 1530: 1523: 1514: 1507: 1503: 1498: 1495: 1494: 1493: 1485: 1476: 1464: 1457: 1449: 1445: 1441: 1439: 1434: 1432: 1427: 1425: 1424:magnetic flux 1419: 1412: 1372: 1366: 1354: 1338: 1335: 1320: 1315: 1313: 1309: 1305: 1301: 1296: 1290: 1288: 1283: 1277: 1272: 1268: 1262: 1255: 1249: 1244: 1226: 1212: 1206: 1190: 1180: 1176: 1171: 1158: 1152: 1146: 1139: 1133: 1127: 1126:magnetic flux 1123: 1114: 1103: 1093: 1091: 1090:magnetic flux 1085: 1077: 1071:Faraday's law 1068: 1066: 1062: 1059:According to 1057: 1055: 1051: 1047: 1045: 1041: 1037: 1033: 1029: 1025: 1021: 1015: 1011: 1006: 1002: 1000: 996: 990: 988: 987:magnetic flux 984: 980: 976: 972: 968: 959: 955: 953: 949: 932: 927: 925: 920: 918: 913: 912: 910: 909: 902: 899: 897: 894: 892: 889: 887: 884: 882: 879: 877: 874: 872: 869: 867: 864: 862: 859: 857: 854: 852: 849: 847: 844: 842: 839: 837: 834: 832: 829: 827: 824: 822: 819: 817: 814: 812: 809: 807: 804: 802: 799: 797: 794: 792: 789: 787: 784: 782: 779: 777: 774: 772: 769: 767: 764: 762: 759: 757: 754: 752: 749: 747: 744: 742: 739: 737: 734: 732: 729: 727: 724: 723: 717: 716: 709: 706: 704: 701: 699: 696: 694: 691: 689: 686: 684: 681: 679: 676: 674: 671: 670: 667: 662: 661: 654: 651: 649: 646: 644: 641: 639: 636: 634: 631: 629: 626: 624: 621: 619: 616: 614: 611: 609: 606: 604: 601: 599: 596: 594: 591: 589: 586: 585: 582: 577: 576: 569: 566: 564: 561: 559: 556: 554: 551: 549: 546: 544: 541: 539: 536: 534: 531: 529: 526: 524: 523:Joule heating 521: 519: 516: 514: 511: 509: 506: 504: 501: 499: 496: 494: 491: 489: 486: 484: 481: 479: 476: 475: 472: 467: 466: 459: 456: 454: 451: 449: 446: 444: 441: 439: 438:Lorentz force 436: 434: 431: 429: 426: 424: 421: 419: 416: 414: 411: 409: 406: 404: 401: 399: 396: 394: 391: 389: 386: 384: 381: 379: 376: 374: 371: 369: 366: 365: 362: 357: 356: 349: 346: 344: 341: 339: 338:Magnetization 336: 334: 331: 329: 326: 324: 323:Magnetic flux 321: 319: 316: 314: 311: 309: 306: 304: 301: 299: 296: 295: 292: 287: 286: 279: 276: 274: 271: 269: 266: 264: 261: 259: 256: 254: 251: 249: 246: 244: 241: 239: 236: 234: 231: 229: 228:Electric flux 226: 224: 221: 219: 216: 214: 211: 209: 206: 204: 201: 199: 196: 194: 191: 190: 187: 182: 181: 176: 173: 171: 168: 166: 165:Computational 163: 161: 158: 156: 153: 151: 148: 146: 143: 142: 141: 140: 136: 132: 131: 128: 125: 124: 120: 119: 116: 114: 113:Lorentz force 108: 106: 102: 97: 95: 91: 87: 83: 79: 75: 71: 67: 63: 59: 55: 51: 50:Faraday's law 47: 40: 36: 32: 28: 23: 19: 7435: 7410:Faraday disc 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Retrieved 6827:HyperPhysics 6826: 6816: 6797: 6791: 6779:. Retrieved 6775:the original 6770: 6760: 6732: 6726: 6702:the original 6684:(1): 31–44. 6681: 6677: 6664: 6644: 6637: 6613: 6592:. Retrieved 6588: 6559: 6540: 6533: 6525: 6521: 6515: 6503:. Retrieved 6492: 6479: 6467:. Retrieved 6456: 6443: 6434: 6409: 6405: 6395: 6381: 6372: 6366: 6355: 6328:. Retrieved 6313: 6306: 6295:the original 6288: 6257: 6235:. Retrieved 6231: 6222: 6202: 6195: 6178: 6160: 6140: 6133: 6122:. Retrieved 6116: 6109: 6095:Felici's law 6070:Eddy current 6053: 6042: 6038: 6034: 6030: 6018: 5695:motional emf 5694: 5692: 5685: 5677: 5668: 5666: 5660: 5656: 5651: 5644: 5640: 5637: 5633: 5629: 5622: 5617: 5608: 5601:motional emf 5600: 5598: 5576: 5572: 5371: 5365: 5343: 5339: 5333: 5299: 5293: 5287: 5281: 5279: 4604: 4600: 4593: 4589: 4582: 4578: 4571: 4567: 4561: 4558: 4552: 4447: 4440: 4436: 4302: 3799: 3793: 3785: 3781: 3577: 3396: 3389: 3385: 3380: 3376: 3369: 3362: 3354: 3350: 3344: 3332: 3328: 3322: 3315: 3308: 3209: 3026: 2762: 2645: 2639: 2629: 2507: 2498: 2492: 2251: 2245: 2238: 2119: 2116: 2110: 2104: 2098: 2096: 2084:scalar field 2078: 2072: 2062: 2054: 2048: 2042: 2036: 2029: 2022: 2008: 2001: 1997: 1987: 1981: 1974: 1964: 1957: 1950: 1947: 1846: 1836: 1826: 1816: 1805: 1801: 1797: 1786: 1782: 1778: 1760: 1702: 1697:conservative 1694: 1683: 1677: 1670: 1661: 1649: 1572: 1562:coil of wire 1559: 1551: 1539: 1528: 1521: 1512: 1501: 1491: 1483: 1474: 1462: 1455: 1442: 1435: 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568:Waveguides 548:Resistance 518:Inductance 298:Ampère law 90:generators 7172:208095922 7070:135524562 7056:: 11–23. 6872:965197645 6735:(1): 48. 6494:Big Think 6330:28 August 6085:Crosstalk 5970:∇ 5967:− 5807:∂ 5797:∂ 5791:− 5743:∂ 5733:∂ 5727:− 5717:∇ 5714:− 5548:⋅ 5537:× 5517:Σ 5514:∂ 5510:∮ 5503:Σ 5495:⋅ 5486:∂ 5476:∂ 5468:Σ 5464:∫ 5460:− 5444:⋅ 5433:× 5405:Σ 5402:∂ 5398:∫ 5238:⋅ 5225:× 5205:∮ 5189:⋅ 5176:× 5163:∮ 5133:⋅ 5125:∮ 5095:⋅ 5082:× 5061:∮ 5024:− 4999:Φ 4878:× 4833:⋅ 4822:× 4791:⋅ 4780:× 4757:× 4726:⋅ 4715:× 4663:⋅ 4652:× 4504:⋅ 4491:× 4470:∮ 4401:⋅ 4388:× 4356:Σ 4353:∂ 4349:∮ 4345:− 4320:Φ 4272:⋅ 4241:× 4159:Σ 4156:∂ 4152:∮ 4148:− 4100:Φ 4053:⋅ 4022:× 3964:Σ 3961:∂ 3957:∮ 3953:− 3927:⋅ 3885:Σ 3882:∂ 3878:∮ 3874:− 3821:Φ 3757:⋅ 3730:× 3676:Σ 3673:∂ 3669:∮ 3665:− 3649:⋅ 3614:Σ 3610:∫ 3557:× 3537:⋅ 3515:∫ 3512:− 3493:× 3465:⋅ 3457:∫ 3434:⋅ 3426:∫ 3414:Φ 3277:⋅ 3242:Σ 3238:∫ 3186:⋅ 3144:Σ 3141:∂ 3137:∮ 3133:− 3117:⋅ 3085:∂ 3075:∂ 3047:Σ 3043:∫ 2997:⋅ 2962:Σ 2958:∫ 2912:⋅ 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7447:Related 7333:Physics 7152:Bibcode 6929:Bibcode 6781:30 July 6737:Bibcode 6686:Bibcode 6619:301–303 6414:Bibcode 6264:623–624 2059:around 1839:by the 1810:is the 1791:is the 1769:is the 1422:is the 1409:is the 1138:surface 942:History 886:Thomson 861:Ritchie 851:Poisson 836:Neumann 831:Maxwell 826:Lorentz 821:Liénard 751:Faraday 736:Coulomb 563:Voltage 538:Ohm law 160:History 52:) is a 27:(right) 7222: 7170: 7097: 7068: 6967: 6895: 6870: 6860: 6804: 6652: 6625: 6552: 6505:3 July 6469:3 July 6458:Forbes 6321: 6210: 6148: 5043:where 4855:since 4526:where 4434:, and 4426:where 3779:where 3578:Here, 3024:where 2328: 1978:, and 1968:is an 1641:where 1385:where 1239:where 1143:whose 1124:, the 1080:right. 871:Singer 866:Savart 846:Ørsted 811:Larmor 801:Kelvin 756:Fizeau 726:Ampère 648:Stator 155:Optics 7360:Farad 7193:(PDF) 7168:S2CID 7142:arXiv 7091:301–3 7066:S2CID 7009:body. 6705:(PDF) 6674:(PDF) 6298:(PDF) 6285:(PDF) 6187:(PDF) 3449:sweep 3373:sweep 2489:Proof 2101:path 1998:Both 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5374:∂Σ 5362:∂Σ 5342:× 5309:∂Σ 5305:∂Σ 5297:∂Σ 5285:∂Σ 4428:∂Σ 3797:. 3375:= 2638:Σ( 2249:. 2094:. 2052:. 1975:∂Σ 1961:, 1824:. 1804:, 1785:, 1549:ΔΦ 1537:ΔΦ 1519:ΔΦ 1510:ΔΦ 1481:ΔΦ 1472:ΔΦ 1453:ΔΦ 1433:. 1426:. 1258:, 1252:Σ( 1159:: 1149:Σ( 1046:. 995:DC 983:or 96:. 88:, 80:, 41:). 7318:e 7311:t 7304:v 7195:. 7174:. 7162:: 7154:: 7144:: 7103:. 7072:. 7060:: 6973:. 6943:. 6939:: 6931:: 6917:B 6901:. 6874:. 6836:. 6810:. 6785:. 6751:. 6747:: 6739:: 6696:: 6688:: 6658:. 6631:. 6597:. 6509:. 6473:. 6428:. 6424:: 6416:: 6334:. 6266:. 6240:. 6216:. 6189:. 6154:. 6127:. 5998:E 5975:E 5945:E 5922:E 5900:E 5878:B 5856:E 5834:A 5810:t 5801:A 5770:E 5746:t 5737:A 5722:E 5711:= 5707:E 5671:. 5661:B 5657:t 5652:E 5645:B 5641:v 5577:l 5575:d 5557:l 5552:d 5545:) 5541:B 5532:m 5527:v 5522:( 5506:+ 5499:d 5489:t 5480:B 5457:= 5453:l 5448:d 5441:) 5437:B 5428:m 5423:v 5418:+ 5414:E 5410:( 5394:= 5389:E 5344:B 5340:v 5334:B 5329:ω 5300:. 5291:Σ 5247:l 5242:d 5234:) 5229:B 5220:l 5215:v 5209:( 5202:= 5198:l 5193:d 5185:) 5180:B 5172:v 5167:( 5142:l 5137:d 5129:E 5104:l 5099:d 5091:) 5086:B 5078:v 5074:+ 5070:E 5065:( 5058:= 5053:E 5029:E 5021:= 5015:t 5011:d 5003:B 4994:d 4968:l 4963:d 4940:t 4935:v 4912:l 4907:d 4886:) 4882:B 4873:t 4868:v 4863:( 4842:l 4837:d 4830:) 4826:B 4817:l 4812:v 4807:( 4804:= 4800:l 4795:d 4788:) 4784:B 4775:l 4770:v 4765:+ 4761:B 4752:t 4747:v 4742:( 4739:= 4735:l 4730:d 4723:) 4719:B 4712:) 4707:l 4702:v 4697:+ 4692:t 4687:v 4682:( 4679:( 4676:= 4672:l 4667:d 4660:) 4656:B 4648:v 4644:( 4623:l 4618:d 4605:t 4601:v 4594:t 4590:v 4583:l 4579:v 4572:t 4568:v 4562:v 4553:v 4536:E 4513:l 4508:d 4500:) 4495:B 4487:v 4483:+ 4479:E 4474:( 4467:= 4462:E 4441:l 4437:v 4432:Σ 4414:. 4410:l 4405:d 4397:) 4392:B 4382:l 4376:v 4371:+ 4367:E 4362:( 4342:= 4336:t 4332:d 4324:B 4315:d 4285:. 4281:l 4276:d 4267:) 4262:) 4257:0 4253:t 4249:( 4245:B 4238:) 4233:0 4229:t 4225:( 4219:l 4213:v 4208:+ 4205:) 4200:0 4196:t 4192:( 4188:E 4182:( 4175:) 4170:0 4166:t 4162:( 4145:= 4138:0 4134:t 4130:= 4127:t 4122:| 4116:t 4112:d 4104:B 4095:d 4067:) 4062:l 4057:d 4048:) 4043:) 4038:0 4034:t 4030:( 4026:B 4019:) 4014:0 4010:t 4006:( 4000:l 3994:v 3987:( 3980:) 3975:0 3971:t 3967:( 3949:( 3945:+ 3941:) 3936:l 3931:d 3924:) 3919:0 3915:t 3911:( 3907:E 3901:) 3896:0 3892:t 3888:( 3870:( 3866:= 3859:0 3855:t 3851:= 3848:t 3843:| 3837:t 3833:d 3825:B 3816:d 3794:Σ 3792:∂ 3786:l 3782:v 3766:l 3761:d 3754:) 3751:) 3746:0 3742:t 3738:( 3734:B 3727:) 3722:0 3718:t 3714:( 3708:l 3702:v 3697:( 3692:) 3687:0 3683:t 3679:( 3662:= 3658:A 3653:d 3646:) 3641:0 3637:t 3633:( 3629:B 3623:) 3620:t 3617:( 3603:t 3599:d 3593:d 3565:) 3561:B 3551:l 3545:v 3540:( 3533:l 3528:d 3523:t 3519:d 3509:= 3506:) 3502:l 3497:d 3490:t 3486:d 3479:l 3473:v 3468:( 3461:B 3454:= 3444:A 3438:d 3430:B 3423:= 3418:B 3409:d 3397:t 3395:d 3390:l 3386:t 3384:d 3381:l 3377:v 3370:A 3368:d 3363:t 3361:d 3355:l 3351:v 3345:l 3343:d 3337:. 3333:l 3329:v 3323:t 3321:d 3316:Σ 3314:∂ 3309:l 3307:d 3286:A 3281:d 3274:) 3269:0 3265:t 3261:( 3257:B 3251:) 3248:t 3245:( 3231:t 3227:d 3221:d 3195:l 3190:d 3183:) 3178:0 3174:t 3170:( 3166:E 3160:) 3155:0 3151:t 3147:( 3130:= 3126:A 3121:d 3110:0 3106:t 3102:= 3099:t 3094:| 3088:t 3079:B 3063:) 3058:0 3054:t 3050:( 3030:0 3027:t 3011:) 3006:A 3001:d 2994:) 2989:0 2985:t 2981:( 2977:B 2971:) 2968:t 2965:( 2951:t 2947:d 2941:d 2934:( 2930:+ 2926:) 2921:A 2916:d 2905:0 2901:t 2897:= 2894:t 2889:| 2883:t 2874:B 2858:) 2853:0 2849:t 2845:( 2833:( 2829:= 2822:0 2818:t 2814:= 2811:t 2806:| 2800:t 2796:d 2788:B 2779:d 2748:A 2743:d 2736:) 2733:t 2730:( 2726:B 2720:) 2717:t 2714:( 2700:t 2696:d 2690:d 2684:= 2678:t 2674:d 2666:B 2657:d 2642:) 2640:t 2615:A 2610:d 2603:) 2600:t 2597:( 2593:B 2587:) 2584:t 2581:( 2567:t 2563:d 2557:d 2551:= 2545:t 2541:d 2533:B 2524:d 2510:Σ 2469:r 2462:3 2458:d 2449:3 2444:| 2434:r 2425:r 2420:| 2413:) 2404:r 2395:r 2390:( 2382:) 2376:t 2368:) 2365:t 2362:, 2354:r 2349:( 2345:B 2335:( 2323:V 2309:4 2305:1 2294:) 2291:t 2288:, 2284:r 2280:( 2275:s 2270:E 2246:Σ 2239:B 2236:Φ 2215:. 2211:A 2206:d 2198:B 2181:t 2177:d 2171:d 2162:= 2158:l 2153:d 2145:E 2120:Σ 2111:Σ 2105:Σ 2103:∂ 2079:E 2073:E 2063:Σ 2061:∂ 2049:Σ 2043:n 2037:Σ 2035:∂ 2030:l 2028:d 2023:Σ 2009:A 2007:d 2002:l 2000:d 1988:Σ 1982:A 1980:d 1965:l 1963:d 1958:Σ 1956:∂ 1951:Σ 1932:A 1927:d 1917:t 1908:B 1885:= 1881:l 1876:d 1868:E 1822:t 1817:r 1808:) 1806:t 1802:r 1800:( 1798:B 1789:) 1787:t 1783:r 1781:( 1779:E 1743:t 1734:B 1721:= 1717:E 1691:. 1684:n 1678:Σ 1676:∂ 1671:Σ 1650:B 1647:Φ 1643:N 1626:t 1622:d 1614:B 1605:d 1598:N 1592:= 1587:E 1573:B 1570:Φ 1566:N 1552:B 1540:B 1529:n 1522:B 1513:B 1502:n 1484:B 1475:B 1468:A 1463:B 1456:B 1418:B 1415:Φ 1395:E 1373:, 1367:t 1363:d 1355:B 1346:d 1336:= 1331:E 1295:B 1282:A 1280:d 1271:A 1267:B 1261:B 1256:) 1254:t 1243:A 1241:d 1227:, 1222:A 1217:d 1210:) 1207:t 1204:( 1200:B 1194:) 1191:t 1188:( 1177:= 1172:B 1153:) 1151:t 1141:Σ 1132:B 1129:Φ 1113:A 1111:d 1107:Σ 993:( 930:e 923:t 916:v 39:G 35:B 31:A

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Knowledge

Faraday's law of induction

Index