3.236. B = Ron//1/1 (2R//)2.
3.237. (a) B 1/2 p,0n1 (1 — x/V x 2 + R2), where x> 0 outside
the solenoid and x < 0 inside the solenoid; see Fig. 23; (b) xo =
R (1— 21)12V 1(1—
5R.
3.238. B = .{(1-411h)11 (1— (h12311)2= 0.3 mT, r (110/431) 21/r, r > R.
3.239. r1 x N/Jt = 8.102.
= 1.0 pWb/m.
(110/47t) =
70 B/6a
3.240.
3.241.
(121 = (120 0/2 = kn/S/2,
• 8
where (Do is the flux of the vec-
0.
for B through the cross-section of
0#
the solenoid far from its ends.
3.242. (I) = (110/4n) 2INh In 1=
0.2
= 8 [Mb.
3.243.
pm = 23-cR3BI110 =
= 30 mA • m2.
3.244.
pm =
d2 =
=0.5 A • m2.
3.245. a B
LOIN (b/a) 7 N;
()
2 (b— a)
(b) P m = 113nIN (a2 ab b 2) = 15 mA • m2.
3.246. (a) B = 1/2p. 0 60)R; (b) p m = 1/4260)R4.
3.247. B = 2/3p.060)R = 29 pT.
3.248. pm = 1/ 5 qR2co; pml M = q/2m.
3.249. B = 0.
3.250. FmlFe = 110 80722 = (v/c)2 = 1.00.10-6.
3.251. (a) F1 = 110.12 /4R = 0.20 mN/m;
(b) F1 = 120/21211 =
= 0.13 mN/m.
3.252. B = ad2aml4RI = 8 kT, where am is the strength of
copper.
3.253. B = (2pgS I I) tan 0 = 10 mT, where p is the density
of copper.
3.254. B
= 0.4 T.
3.255. (a) F = 4.0.1101n (412 — 1) = 0.40 p.N;
(b)
A =
= (11 o all0/n) In )(21
1)/(2ri — 1)] = 0.10 J.
3.256. R Yµ0/s0 (ln i)/n = 0.36 kS2.
3.257. F1 = p,01.2/3-1, 2R.
3.258. F1= 4
2111 2 In (1 + b/a).
3.259. F1 = /3 1/21..t 0.
3.260. In all three cases F1 = (B: — B:)/2110. The force is directed to the right. The current in the conducting plane is directed
beyond the drawing.
3.261. Ap = IBla = 0.5 kPa.
3.262. p = p.0/2 /8n2R2.
3.263. p = 1/2p.0n212•
0
Fig. 23.
,Z'/?