Download PDF by Jack Vanderlinde: Classical electromagnetic theory

By Jack Vanderlinde

ISBN-10: 1402026994

ISBN-13: 9781402026997

ISBN-10: 1402027001

ISBN-13: 9781402027000

The variety of pupil routines has been elevated via forty five over the former edition.

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28 Classical Electromagnetic Theory serves as a scalar potential for the magnetic induction field. 17). Use the scalar potential to find the magnetic induction field on the central axis. 17: The observer is directly below the center of the loop. Solution: We first find Ω. 2) (the constant term may of course be dropped without loss). 16), the scalar potential of the current loop becomes a building block for a number of other problems whose currents can be decomposed into current loops. 16: Find the scalar magnetic potential along the axis of a solenoid of length L with N closely spaced turns, carrying current I.

We can however evaluate A by equating its curl to the expression for B as found in (1–32) and integrating. 4) µ0 I ln r + const. 6) with Λ an arbitrary scalar function. 6) provides us with a useful form of the expression for the vector potential; for, if we consider that it governs the vector potential produced by a filament of current dI extending infinitely in the z-direction at r = 0, dAz (r ) = − µ0 ln r dI 2π (1–54) The vector potential of the entire current considered as a superposition of the filaments located ar r becomes, with the replacement dI = Jz (r )dS , Az (r ) = − µ0 2π Jz (r ) ln |r − r | dS which may be integrated over arbitrary cross-sections.

The line integral of the electric field along the wire is precisely cancelled by the line integral of the field through the battery. The force communicated to the charges is well defined only as a line integral. The line integral around the loop of the total force per charge is called the electromotive force, or EMF, which we give the symbol E. F ·d (3–1) E= q —49— 50 Classical Electromagnetic Theory The name is rather a misnomer because the EMF is certainly not a force, rather, it is the work that would be performed on a unit charge in travelling around the loop.

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Classical electromagnetic theory by Jack Vanderlinde

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