Irodov – Problems in General Physics

3.45. cp ;--.:.: -I- --:r/ .-- - (1 x ) , E,•,=:-.1

aiR2

,, If xR,

2e 0 1 1 s^2 -^1 -^112 2e^0 (x^2 + R^2 )3," '

then cp ,-...z.-, ± 40 :x2 and E ,--:-.', 2318 P , oxswhere p= nR^2 al. In the

formulas for the potential cp the plus sign corresponds to the
space adjoining the positively charged plate and the minus sign
to the space adjoining the negatively charged plate.

3.46. (a) F = 0; (b) F = n _XP 2 ; (c) F -= .., 4

3p2^4 ngor^ Itsr^2

3.47. F = 2neot 4 = 2.1.10

-16 N.

3.48. cp = —axy const.

3.49. cp = ay (3 — x 2 ) + const.

3.50. cp = —y (ax^ bz)^ const.

3.51. p = 6e 0 ax.

3.52. p = 2e 0 AT/c/ 2 ; E = pdieo.

3.53. p = —6e 0 a.

3.54. q= 41 17 neokx.

2

3.55. A= q

16aso/

3.56. (a) F = (2 i8!: 3112 ) q2 ; (b) E=2 (1

3.57. F = (2 (^) 323t801 2 q2
3.58. F = (^3132) 327[8,0 (^) '
3.59. a -=
ql
2 7t (1 2 + r2)- 3/2 t qind =^ q•
3.60. (a) F1= 47t)'^82 0/ ; (b) a =^ (^4 x2).
3.61. (a) a =^ (b)a (r) 2n 1712+r2^
3.62. (a)
(/ 2 + R 2 ) 3 / 2
— (b) E= , 0
lq
422 L (^8 41) + (^1) /4 (R/ 1 )93/2
1
`= 471E0 R\ (^1) 1/1+4 (i/R) 2
3.63. (p = (^) 4neol •
3.64. cp=
1 1 _L 1
4aeo Ri - Rg 1-
11r-114 if a < r < b,
3 ' 65 ' q (^2) a q 1 ; (^) (1—bla) r if r > b.
3.66. (a) E23 = Acp/d, E (^12) = E 3 4 = 112 E23; (b) al =
= 1 /2 8 04M, az = I as I = 3 /2 8 04/d.
3.67. q 1 = —q (1 — x)I1, q 2 = —qx/l. Instruction. If the charge
q is imagined to be uniformly spread over the plane passing through
q
5 lig 1 neo12