4.198. Since t> 7', where 7' is the period of oscillations, W
= 1 /21/ Ego/RE^2 maR^2 t = 5 kJ.
4.199. B = Bm sin kx• sin wt, where Bm Em, with B D, = Ernie.
4.200. S x = 1 / 4 cocEl sin 2kx• sin 2wt, (Sx ) = 0.
4.201. Wm/We = 1 / 8 calo w 2 R 2 = 5.0.10-1b
4.202. We/Wm = 1 / 8 6,11 0 (0 2 R 2 = 5.0.10-15
4.204. 4 :Ds = I 2 R.
4.205. S = I 2 1/ mi2eU/4a 2 eor 2.
4.207. To the left.
4.208. (ID = V I.
4.209. (0) = 1 / 217 0 / 0 cos cp.
4.211. The electric dipole moment of the system is p = /er =- i
= (elm) Mrc, where M is the mass of the system, rc is the radius
vector of its centre of inertia. Since the radiation power P oc p 2 occc r t, and in our case rc = 0, P = 0 too.
4nEo0 6)
4.212. (P)=- =5 .10-15 W.4.213. P =1 2 4 qe^2 \ 2
(4neo) 3 3c 3 mR2 /
4.214. AW 7=4--ile4q2
(4neo) 3 3c 3 m 2 vb 3 •
4.215. AW/T = 1 / 3 e 3 B/e 0 c 3 m 2 = 2.10-18.
4.216. T = Toe-- a't, where a = 1 / 3 e 4 B 2 /a8 0 c 3 m 3. After
r 2.5 s for the electron,
1 1.6.10^1 ° s = 0.5.10^3 years for the proton.
4.217. S 1 /S 2 = tan 2 (o)//c) = 3.
4.218. (a) Suppose that t is the moment of time when the particle
is at a definite point x, y of the circle, and t' is the moment when
the information about that reaches the point P. Denoting the observed
values of the y coordinate at the point P by y' (see Fig. 4.40), we
shall writeThe sought acceleration is found by means of
tiation of y' with respect to t':
dy' = dy dy dt d 2 y d dy'
dt' dt' = dt dt" dt' = 2 dt' dt dt'the double differen-=- v_^2 vIc—yIR^
R (1—vy/cR) 3 '
where the following relations are taken into account: x = R sin wt,
y = R cos wt, and w = v/R.
(b) Energy flow density of electromagnetic radiation S is pro-
portional to the square of the y projection of the observed accelera-
tion of the particle. Consequently, S 1 /S 2 = (1 v/c) 4 /(1 — v/c) 4.
4.219. (P) = 8 / 3 ar 2 S 0.
4.220. (w) = 3 /8Po/ar 2 c.
4.221. P = 1 / 6 p 2 6) 4 /neoc 2.to —=334