3.1. F/F 4*1042 1*1036; q/m = 0,86*10-10 /
3.2. 2*1015
3.3. dq/dt = 3/2 a sqrt(2πε0mg/l)
3.4. q3 = -q1q2/(sqrt(q1)+sqrt(q2))2, r3 = (r1*sqrt(q2)+r2*sqrt(q1))/(sqrt(q1)+sqrt(q2))
3.5. ΔT = qq0/(8π2ε0r2)
3.6. E = 2,7i-3,6j, E = 4,5 /
3.7. E = ql/(sqrt(2)*πε0(l2+x2)3/2)
3.8. E = q/(2π2ε0R2)
3.9. E = ql/(4πε0(r2+l2)3/2)
3.10. E = 3qR2/(4πε0x4)
3.11. F = qλ/(4πεoR)
3.12. ) E = λo/(4εoR); ) E = λoR2/(4εo(x2+R2)3/2)
3.13. ) E = q/(4πε0r*sqrt(a2+r2)); ) E = q/(4πε0r*sqrt(r2-a2))
3.14. E = (λ*sqrt(2))/(2πε0y). E 45°
3.15. ) E = λ*sqrt(2)/(4πε0R) ) E = 0
3.16. E = -1/3 ar/ε0
3.17. E = -1/3 kσoo, k - z
3.18. E = -1/6 aR20
3.19. || = 1/2 λR/ε0.
3.20. || = q(1-1/sqrt(1+(R/l)2))/εo.
3.21. p = 280 ; p = 80
3.22. E = λ/πε0l
3.24. = 4πRa
3.25. T > a/bR
3.26. q = 2πR2α, E = 1/2α/εo
3.27. E = ρ0(1-e-αr3)/(3ε0αr2)
3.28. E = 1/3 aρ/ε0
3.30. Δφ = q(1-1/sqrt(1+(a/R)2))/(2πε0R)
3.31. φ12 = 5
3.32. φ = 1/2 σR/ε0, E = 1/4 σ/ε0
3.33. φ = σl(sqrt(1+(R/l)2)-1)/2ε0, E = σ(1-l/sqrt(l2+R2))/2ε0
3.34. φ = σR/πε0
3.35. E = -a
3.36. ) E = -2a(xi-yj); ) E = -a(yi+xj). i,j - x,y
3.37. E = -2(axi+ayj+bzk), E = 2 sqrt(a2(x2+y2)+b2z2)
3.38. ) φo = 3q/(8πεoR); ) φ = φo(1-r2/(3R2)), r ≤ R
3.39. E = sqrt(Er2+Eυ2)
3.40. Ez = p(3 cos2υ-1)/(4πε0r3), E = p(3 sin υ cos υ)/(4πε0r3)
3.41. R = (p/4πε0E0)1/3
3.42. φ ≈ λl/(2πεor) cos υ, E ≈ λl/(2πεor2)
3.43. φ = qlx/(4πεo(R2+x2)3/2), Ex = - ql(R2-2x2)/(4πεo(R2+x2)5/2)
3.45. &phi ≈ ± σl/(2εo)*(1-x/sqrt(x2+R2)), E ≈ &sigmalR2/(2εo(x2+R2)3/2)
3.46. ) F = 0; ) F = -λp/(2πε0r2); ) F = λp/(2πε0r2)
3.47. F = 2,1*10-16 H
3.48. φ = -axy+const
3.49. φ = ay(y2/3-x2)+const
3.50. φ = -y(ax+bz)+const
3.51. ρ = 6ε0ax
3.52. ρ = 2εoΔφ/d2, E = ρd/εo
3.53. ρ = -6ε0a
3.54. q = 4l sqrt(πε0kx)
3.55. A = q2/(16πε0l)
3.56. ) F = (2sqrt(2)-1)q2/(8πεol2); ) E = 2[1-1/(5sqrt(5))]q/(πεol2)
3.57. F = (2sqrt(2)-1)q2/(32πεol2)
3.58. F = 3p2/(32πεol4)
3.59. σ = -ql/(2π(l2+r2)3/2), q = -q
3.60. ) F1 = λ2/(4πε0l); ) = lλ/(π(l2+x2))
3.61. ) σ = λ/(2πl); ) σ(r) = λ/(2π sqrt(l2+r2))
3.62. ) σ = lq/[2π(l2+R2)3/2]; ) E = 1/4πε0 q/(4l2[1+1/4 (R/l)2]3/2), φ = 1/4πε0 q/R (1-1/sqrt(1+4(l/R)2))
3.63. φ = q/(4πε0l)
3.64. φ = q(1/r-1/R1+1/R2)/(4πε0)
3.66. ) E23 = Δφ/d, E12 = E34 = 1/2 E23; ) |σ1| = σ4 = 1/2 ε0Δφ/d, σ2 = |σ3| = 3/2 ε0Δφ/d
3.68. dF/dS = 1/2 δ20
3.69. F = 0,5
3.72. F = 3βp2/(4π2εol7)
3.73. ) x = R/sqrt(2); ) x = 1,1 R (), x = 0,29 R ()
3.74. P = ((ε-1)qr)/(4επr3), q' = -(ε-1)q/ε
3.76. q' = -q(ε-1)/ε, q' = q(ε-1)/ε
3.77. . .
3.78. E = 5,2 /, α = 74°, σ' = 64 /2
3.79. ) ∫EdS = (ε-1)/ε*πR2Eo cos υ; ) ∫Ddr = -εo(ε-1)lEo sin υ
3.80. ) E = ρl/ε&epsilon0 l < d ...
3.81. E = ρr/3ε0ε r < R
3.82. E = -dP/(4ε0R)
3.83. E = -P0(1-x2/d2)/ε0, U = 4dP0/3ε0
3.84. ) E1 = 2εE0/(ε+1), E2 = 2E0/(ε+1), D1 = D2 = E1 = 2εε0E0/(ε+1); ) E1 = E0, E2 = E0/ε, D1 = D2 = &epsilon0E0
3.85. ) E1 = E2 = E0, D1 = ε0E0, D2 = εD1; ) E1 = E2 = 2E0/(ε+1), D1 = 2ε0E0/(ε+1), D2 = εD1
3.87. ρ = 1,6 /3
3.89. ) σ' = -ql(ε-1)/(2πr3(ε+1)) ) q' = -q(ε-1)/(ε+1)
3.91. D = q/2π(1+ε)r2 - , D = εq/2π(1+ε)r2 - ; E = q/2πε0(1+ε)r2, φ = q/2πε0(1+ε)r -
3.93. σ' = ql(ε-1)/2πr3ε
3.95. ρ' = -2&alpha
3.96. ) E = -P/3ε0
3.99. E = -P/2ε0
3.101. C = (4πε0εR1)/(1+(ε-1)R1/R2)
3.102. F = 0,9*10-19
3.103. NA ≈ 6,4*1023 -1
3.104. a) C = εo21)S/(d ln(ε21)); ) ρ' = -q(ε21)/(dSε2)
3.105. C = 4πεoa/ln(R2/R1)
3.108. C ≈ πε0/ln(b/a)
3.109. C ≈ 2πεo/ln(2b/a)
3.110. C ≈ 2πε0εa
3.111. C ≈ 4πεoa
3.112. ) C = C1+C2+C3; ) C = C
3.114. U <= 9
3.115. U = 10
3.116. Cx = 0,62C
3.117. U1 = 10 , U2 = 5
3.118. U1 = (ξ21)(1+C1/C2), U2 = (ξ12)(1+C2/C1)
3.120. φA - φB = ξ(C2C3-C1C4)/((C1+C2)(C3+C4)). C1/C2 = C3/C4
3.121. q = 0,06
3.122. q1 = ξC2, q2 = -ξC1C2/(C1+C2)
3.123. q1 = -24 , q2 = -36 , q3 = +60
3.124. φAB = (C2ξ2-C1ξ1)/(C1+C2+C3)
3.127. ) W = (sqrt 2 + 4)q2/4πε0a; ) W = (sqrt 2 - 4)q2/4πε0a; ) W = -q2sqrt 2/4πε0a;
3.129. W = -q2/8πε0l
3.131. ΔW = -0,03
3.132. Q = ξ2CCo/(2C+Co)
3.134. W = W1+W2+W12
3.135. ) W = 3q2/20πε0R; ) W1/W2 = 1/5
3.136. W = 27
3.137. A = (q2/8πε0)(1/R1-1/R2)
3.138. A = q(q0+q/2)(1/R1-1/R2)/(4πε0)
3.141. ) A = q2(x2-x1)/2ε0S; ) A = ε0SU2(x2-x1)2x1x2
3.142. ) = 1,5 ; ) = 0,8
3.143. Δp = 7 = 0,07
3.147. I = 0,5
3.148. I ≈ 0,11
3.150. ) 5/6R ) 7/12R ) 3/4R
3.154. R = (ρ/2πl) ln(b/a)
3.155. R = ρ(b-a)/(4πab). b → ∞ R = ρ/(4πa)
3.156. ρ = 4πΔtab/(b-a)C ln η
3.158. ) j = 2alU/ρr3; ) R = ρ/4πa
3.159. ) j = lU/2ρr2ln(l/a); ) R1 = (ρ/π) ln(l/a)
3.160. I = 1,5
3.163. I = 5
3.167. q = ε0I(ε2ρ21ρ1)
3.168. ρ = 2ε0U(η-1)/d2(η+1)
3.169. ) R1 = 2πα/S2; ) E = 2παI/S2
3.171. ρ = 1,4*1013 *
3.172. I = [(η-1)ξ/R]e-ηt/RC
3.173. U = 2,0
3.176. ) I = α; ) φA - φB = 0
3.177. φAB = -0,5
3.178. I1 = 1,2 , I2 = 0,8
3.179. U = U0Rx/[Rl+R0(l-x)x/l]; R >> R0 U ≈ U0x/l
3.180. ξ = (ξ1R22R1)/(R1+R2), Ri = R1R2/(R1+R2)
3.181. I = 0,02 , -
3.182. ) I1 = 0,06 ; ) φAB = 0,9
3.183. I = [ξ(R2+R3)+ξ0R3]/[R(R2+R3)+R2R3]
3.184. φAB = -1,0
3.185. I1 = 0,2
3.189. ) Q = 4/3q2R/Δt; ) Q = 1/2 ln(2)q2R/Δt
3.190. R = 3R0
3.193. I = U/2R; P = U2/4R; η = 1/2
3.197. R = R1R2/(R1+R2); Q = (ξ1R22R1)2/4R1R2(R1+R2)
3.199. Q = 60
3.203. ) q = qoe-t/εoερ; ) Q = (1/a-1/b)qo2/(8πεoε)
3.205. ) I = (U0/R)e-2t/RC; ) Q = 1/4 CU02
3.207. p = 0,40 *
3.210. E = 32 /, Δφ = 0,80
3.214. ) ni = 6*109 -3*-1; ) n = 6*107 -3
3.215. t = 13
3.219. ) B = 6,3 ; ) B = 2,3
3.220. B = nμ0I tg(π/n)/2πR
3.221. B = 0,10
3.222. B = 28
3.223. ) B = μ0I((2π-φ)/a+φ/b)/4π; ) B = μ0I(3π/4a+sqrt(2)/b)/4π
3.224. B ≈ μ0hI/4π2Rr, r -
3.225. B = μI/(π2R)
3.226. ) B = (μ0/4π)(πI/R); ) B = (μ0/4&pi)(1+3π/2)I/R; ) B = (μ0/4π)(2+π)I/R
3.227. B = 2,0
3.228. ) B = 30 ; ) B = 0,34 ; ) B = 0,11
3.229. ) B = μ0i/2; ) B = μ0i B = 0
3.230. B = {μojx - ; μojd - }
3.232. μ0I
3.233. B = 1/2 μ0[jr] r ≤ R
3.234. B = 1/2μo[jl], ..
3.235. j(r) = (b/μ0)(1+α)rα-1
3.236. B = μ0nI/sqrt(1+(2R/l)2)
3.237. ) B = 1/2 μ0nI(1-x/sqrt(x2+R2), x > 0 x < 0 ; ) x0 = R(1-2η)/2*sqrt(η(1-η)) ≈ 5R
3.240. = 1,0 /
3.242. = 8
3.243. pm = 30 *2
3.244. pm = 0,5 *2
3.245. ) B = 7 ; ) pm = 15 *2
3.246. ) B = 1/2 μ0σωR; ) pm = 1/4 πσωR4
3.247. B = 29
3.248. pm = 1/5 qR2ω; pm/M = q/2m
3.250. F/F = 1,00*10-6
3.251. ) F1 = 0,20 /; ) F1 = 0,13 /
3.252. B = 8
3.253. B = 10
3.254. B = 0,4 T
3.255. ) F = 0,40 ; ) A = 0,10
3.256. R = 0,36
3.258. F1 = μ0/4π 2I1I2/b ln(1+b/a)
3.260. F1 = (B12-B22)/2μ0
3.261. Δp = 0,5
3.263. p = 1/2μon2I2
3.264. I = sqrt(2F0nR)
3.267. n = 2,5*1028 -1; 1:1
3.268. u0 = 3,2*10-3 2/(*)
3.269. ) F = 0; ) F = (μ0/4π)2Ipm/r2, F ↑↓ B; ) F = (μ0/4π)2Ipm/r2, F ↑↓ r
3.270. F = (μ0/4π)3πR2Ipm/(R2+x2)5/2
3.271. F = 9
3.274. ) ∫HdS = π(μ-1)R2B cos υ/(μμo); ) ∫Bdr = (1-μ)Bl sin υ
3.276. . .
3.277. B = μ1μ2I/((μ12)πr)
3.279. B = 3Boμ/(2+μ)
3.281. H ≈ 0,10 /
3.282. b << R μ ≈ 3,7*103
3.284. H ≈ 0,26 /, B ≈ 1,25 μ ≈ 4*103
3.285. F ≈ 1/2 χVB20
3.286. ) xm = 1/sqrt(4a); ) χ = 3,6*10-4
3.288. ξ i = By*sqrt(8ω/a)
3.289. I = Bvl/(R+Rμ), Rμ = R1R2/(R1+R2)
3.290. ) Δφ = 3,0 ; ) Δφ ≈ 20
3.293. I = α/r, α = 1/2 μ0lvI/πR
3.294. ξi = μo/(4π)*2Ia2v/(x(x+a))
3.296. v = (mgR sin α)/(B2l2)
3.297. w = g sin α/(1+l2B2C/m)
3.300. q = (μ0aI)/(2πR)*ln((b+a)/(b-a)), .. L
3.301. ) I = μ0I0v ln(b/a)/(2πR); ) F = v(μ0I0 ln(b/a)/2π)2/R
3.302. ) s = vomR/(l2B2); ) Q = 1/2mvo2
3.303. v = F(1-e-αt)/αm, α = B2l2/mR
3.304. ) - , ; ) - ; ) - ; ; ) "" -
3.305. I = 0,5
3.307. ξi = 12
3.308. E = 1/2 μ0nIr r < a, E = 1/2 μ0nIa2/r r > a
3.309. I = 2
3.310. E = 1/2 ab(η-1)/(η+1)
3.311. ω = -qB(t)/2m
3.313. Q = 1/3a2τ3/R
3.317. t = 1,5
3.318. τ = 0,7
3.319. L1 = 0,26 /
3.320. L = μ0/2π * μN2a ln(1+a/b)
3.321. L1 = 25 /
3.323. ) I = πa2B/L; ) A = 1/2π2a4B2/L
3.324. I = 2
3.326. I = ξ[1+(η-1)e-tηR/L]/R
3.327. I = ξ/R (1-e-tR/2L)
3.328. I1 = ξL2/(R(L1+L2)), I2 = ξL1/(R(L1+L2))
3.329. L12 = μ0b/2π ln(1+a/l)
3.330. L12 = μ0μhN/2π ln b/a
3.331. ) L12 ≈ 1/2μoπa2/b; ) 21 = 1/2μoπa2I/b
3.334. I2 = αL12(1-e-tR/L2)/R
3.335. Q = 3
3.341. w/w = 1,1*10-15
3.347. ) j = -j; ) I = q/εoερ
3.352. ) j = 3qv/(4πr3); ) j = -qv/(4πr3)
3.356. .
3.357. .
3.358. ∇ x E = [ωB]
3.361. ρ = -0,08 /3; σ = 2 /2
3.367. ) E' = 9 /; α' ≈ 51°; ) B' = 14
3.370. B' ≈ 0,15
3.371. E = Exi+Eyj
3.372. v = 16 /
3.374. ) x = 2E0/a; ) w = qE0/m
3.376. w = eE/(m0(1+T/m0c2)3)
3.377. ) tg ν = eEt/m0v0 sqrt(1-(v0/c)2); ) vx = v0/sqrt(1+(1-v02/c2)(eEt/m0c2)2)
3.378. α = 30°
3.379. ) v = 100 /, T = 6,5 , ) v = 0,51 c, T = 4,1
3.380. ) p = qrB; ) T = moc2(sqrt(1+(qrB/moc)2)-1); ) ω = c2/(r(1+(moc/qrB)2))
3.382. Δl = 2,0
3.383. q/m = 8π2U/(l2(B2-B1)2)
3.384. r = 2ρ|sin φ/2|, ρ = mv sin α/(eB), φ = leB/(mv cos α)
3.385. r = aev0/b, b = μ0eI/(2πm)
3.386. v = U/(rB ln(b/a)), q/m = U/(r2B2ln(b/a))
3.387. ) yn = (2π2mEn2)/(qB2); ) tg α = (v0B)/(2πEn)
3.389. F = 20
3.390. Δl = 6
3.393. U = 2 e/m ((μ0I)/(4π))2ln(a/b)
3.396. U ≥ 0,10
3.397. ) T = 12 ; ) ν = 20
3.400. ω = ω0/sqrt(1+at), ω0 = qB/m, a = qBΔW/πm2c2
3.401. v = 1/2 rqB/m, ρ = r/2