Irodov – Problems in General Physics

3.351. fd-={

1 / 2 :Eir for r < R,

112 BR^2 Ir for r > R.

Here h = p,on/mo) 2 sin cot.

3.352. (a) jd = 42 itrvq 3 ; (b) jd^

3.353. xn,=-. 0, id max — 4,,qva 3 •

3.354. H— q Evri 4nr 3 •

3.355. (a) If B (t), then V X E —OBI& 0. The spatial
derivatives of the field E, however, may not be equal to zero
(V x E 0) only in the presence of an electric field.
(b) If B (t), then V X E = 0. But in the uniform
field V x E = 0.
(c) It is assumed that E = of (t), where a is a vector which is
independent of the coordinates, f (t) is an arbitrary function of time.
Then —awat = V X E = 0, that is the field B does not vary with
time. Generally speaking, this contradicts the equation V x H =
= apiat for in this case its left-hand side does not depend on time
whereas its right-hand side does. The only exception is the case
when f (t) is a linear function. In this case the uniform field E can
be time-dependent.
3.356. Let us find the divergence of the two sides of the equation
V X H = j °plat. Since the divergence of a rotor is always equal

to zero, we get 0 = V•j + 4F (V •D). It remains to take into

account that V•D = p.

3.357. Let us consider the divergence of the two sides of the

first equation. Since the divergence of a rotor is always equal to

zero, V • (mat) = 0 or --aa -F (V•B) = 0. Hence, V•B = const which

does not contradict the second equation.

3.358. V X E

3.359. E' =

3.360. a = eovB = 0.40 pC/m^2.

3.361. p = —2eo)B= —0.08 nC/m 3 , a = eoczo)B= 2 pC/m 2.

3.362. B=

[r]

[yr] r 3 •

3.364. E' = br/r 2 , where r is the distance from the z' axis.

3.365. B' = c2r2

a [rv]

' where r is the distance from the z' axis.

3.367. (a) E' = E V 132 c°82 a VO 2 = 9 kV/m; tan a'

whence a 51'; (b) B' —

PE sin a

-14 IA.

c171-132

qv

4nr 3

tan a

V 1 —,P2

320