Introduction to electrodynamics
Features a clear, accessible treatment of the fundamentals of electromagnetic theory. Its lean and focused approach employs numerous examples and problems.
Carefully discusses subtle or difficult points. Contains numerous, relevant problems within the book in addition to end of each chapter problems and answers.
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These corollaries are analogous to those for the gradient theorem. We shall
develop the parallel further in due course. Example 8 Suppose v = (2x2 + 3y2)j +
(4yz2)k. Let's check Stokes' theorem for the square surface shown in Fig. 1.34.
Here V X v = (4z2 - 2x)i + 2z& and da = dy dz i (In saying that da points in the x
direction, we are committing ourselves to a counterclockwise line integral. We
could as well write da = — dy dz i, but then we would be obliged to go clockwise.)
Since x = 0 ...
[This is tough, so I'll give you a start: 1 B, S-kR3 BdT Write B as (V X A), and apply
Problem 1.61(b). Now put in (5.57), and do the surface integral first, showing that
1 4 — da. = — xr *. 3 (see Fig. 5.58).] (b) Show that the average magnetic field
due to steady currents outside the sphere is the same as the field they produce at
the center. Problem 5.49 I worked out the multipole expansion for the vector
potential of a line current because that's the most common type, and in some
... what this freedom entails. Suppose we have two sets of potentials, ( V, A) and (
V" , A ' ), which correspond to the same electric and magnetic fields. By how much
can they differ? Write A' = A + a and V = V + /3 Since the two A's give the same B,
their curls must be equal (7.63), and hence V Xa = 0 We can therefore write a as
the gradient of some scalar: a = VX The two potentials also give the same E, so (
7.64) requires that da or ...
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LibraryThing ReviewUser Review - astropi - LibraryThing
This is one of my all-time favorite science books! Does a BRILLIANT job of presenting the physics, and reviews the basic math (divergence, Stoke's Theorem, etc). This book is a MUST for anyone in ... Read full review
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