By Jack Vanderlinde
This e-book is a self contained direction in electromagnetic conception appropriate for senior physics and electric engineering scholars in addition to graduate scholars whose prior has no longer ready them good for books comparable to Jackson or Landau and Lifschitz. The textual content is liberally sprinkled with labored examples illustrating the applying of the idea to numerous actual difficulties. during this re-creation i've got endeavored to enhance the accuracy and clarity, further and extra clarified examples, further sections on Schwarz-Christoffel mappings, and to make the publication extra autonomous further an appendix on orthogonal functionality expansions and further the derivation of Bessel services and Legendre polynomials in addition to derivation in their producing services. The variety of pupil workouts has been elevated by means of forty five over the former edition.
This ebook stresses the solidarity of electromagnetic conception with electrical and magnetic fields constructed in parallel. SI devices are used all through and significant use is made from tensor notation and the Levi-Cevita image. To extra heavily show the parallelism, large use is made from the scalar magnetic power quite 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 equipped in appendices.
For information about ideas handbook, please touch the writer Jack Vanderlinde at: email@example.com or see web site www.unb.ca/fredericton/science/physics/jvdl.
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So long as the magnetic ﬁeld intensity, B, is uniform over the area of the loop, there is no net force, hence the torque is independent of origin. 3 Potential Energy The potential energy W of a dipole in a ﬁeld derives primarily from its orientation in the ﬁeld. Not surprisingly, when the dipole is parallel to the ﬁeld, its potential energy is lowest. Since, for a conservative force F = −∇W , we deduce immediately from (2–45) that the magnetic energy is given by W = −m · B (2–48) The case of the electric dipole in an electric ﬁeld is not quite so obvious from our work.
We apply the divergence theorem (20) to the ﬁrst integral to get − µ0 4π ∇ · J(r ) r−r d3 r = − µ0 4π J(r ) · dS r−r (1–48) Now, the volume of integration was supposed to contain all currents so that no current crosses the boundary to the volume meaning that (1–48) also vanishes. If we wish to have non-zero current densities in the problem extending over all space, we take our volume of integration over all space. It suﬃces that J diminish as |r − r |α with α < −1 or faster as r → ∞ to make the integral vanish.
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. ) In fact, since, according to (1–43) and to the chagrin of many physicists whose theories predict the existence, there are no magnetic charges (monopoles) analogous to electric charges, B has zero divergence.