By Jack Vanderlinde

This e-book is a self contained path in electromagnetic thought appropriate for senior physics and electric engineering scholars in addition to graduate scholars whose earlier has no longer ready them good for books reminiscent of Jackson or Landau and Lifschitz. The textual content is liberally sprinkled with labored examples illustrating the appliance of the speculation to numerous actual difficulties. during this re-creation i've got endeavored to enhance the accuracy and clarity, additional and additional clarified examples, further sections on Schwarz-Christoffel mappings, and to make the booklet extra autonomous further an appendix on orthogonal functionality expansions and additional the derivation of Bessel features and Legendre polynomials in addition to derivation in their producing services. The variety of scholar workouts has been elevated by way of forty five over the former edition.

This publication stresses the solidarity of electromagnetic conception with electrical and magnetic fields built in parallel. SI devices are used all through and significant use is made up of tensor notation and the Levi-Cevita image. To extra heavily show the parallelism, huge use is made up of the scalar magnetic power relatively in facing the Laplace and Poisson equation. eighty five labored difficulties illustrate the idea. Conformal mappings are handled in a few aspect. suitable mathematical fabric is supplied in appendices.

For information about ideas handbook, please touch the writer Jack Vanderlinde at: jvd@unb.ca or see site www.unb.ca/fredericton/science/physics/jvdl.

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**Example text**

A) The electrons co-rotate is the number of dipoles per unit area diametrically opposed, (b) the electrons and p is the mean dipole moment of these dipoles. 9). 2-18 Find an expression for the force be- 2-23 In the Stern-Gerlach experiment, tween two dipoles p1 , and p2 , separated atoms with diﬀerently oriented magnetic moments are separated in pasby r. sage through a nonhomogeneous mag2-19 Find an expression for the force netic ﬁeld produced by a wedge-shaped between a quadrupole with components magnet.

15. 1) Chapter 1 - Static Electric and Magnetic Fields in Vacuum 23 Interestingly, so long as the loop remains within the torus, up or down displacement makes no diﬀerence. The ﬁeld is independent of z but decreases radially as 1/r . 5 The Magnetic Vector Potential It would be convenient if B could generally be derived from a scalar potential, much in the fashion of the electric ﬁeld. Unfortunately, since the curl of B is not generally zero, B cannot generally be expressed as the gradient of a scalar function.

I) (i) qi r rm ∂2V + · · · (2–50) ∂x ∂xm where the superscript (i ) on the coordinates indicates the charge to which the coordinate belongs. Since the external ﬁeld cannot have charges at the locations r (i) as these positions are already occupied by the charges subjected to the ﬁeld, we have ∇ · E = ∇2 V = 0, which we use to rewrite W as follows: ∂2V + ··· ∂x ∂xm 2 (i) (i) ∂ V = QV − p · E + 16 − r(i)2 ∇2 V · · · qi 3x xm ∂x ∂xm ∂2V (i) (i) = QV − p · E + 16 − δ m r(i)2 ··· qi 3x xm ∂x ∂xm ∂2V = QV − p · E + 16 Q m ··· ∂x ∂xm W = QV + p · ∇V + 1 6 (i) (i) 3qi x xm (2–51) (2–52) (2–53) (2–54) We assume summation over repeated indices in (2–54).