3.45. cp ;--.:.: -I- -- :.-- r/ - (1
x
) , E,• , =:-. 1
aiR2
,, If xR,
2e0
1 1 s 2-1- 112
2e0 (x2 + R2)3," '
then cp ,-. ..z.-, ± 40: x2 and
E ,--:- .' , 2318 P oxs , where p= nR2al. 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
4ngor
Itsr2
3p2
4
3.47. F = 2neot = 2.1.10 -16 N.
3.48. cp = —axy const.
3.49. cp = ay (3 — x2 ) + const.
3.50. cp = —y (ax
bz)
const.
3.51. p = 6e0ax.
3.52. p = 2e0AT/c/2; E = pdieo.
3.53. p = —6e0a.
3.54. q= 41 17 neokx.
2
3.55. A= q
16aso/
3.56. (a) F = (2 i
8!:311 2 ) q2 ; (b) E= 2 (1
3.57. F = (2
q2
323t8012
3.58. F = 3132 327[8,0 '
3.59. a -=
ql
27t (12 r2)3/2 t qind =
q•
+
3.60. (a) F1= 47t )'8 20/ ; (b) a = (4x2) .
3.61. (a) a =
(b)a (r) 2n 1712+r2
3.62. (a)
(/2 + R2)3/2
—
(b) E= , 0
lq
42L8 41
2
+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 - 1- Rg
11r-114 if a < r < b,
3'65' q2
a q1;
(1—bla) r if r > b.
3.66. (a) E23 = Acp/d, E12 = E34 = 112 E23; (b) al =
= 1/2804M, az = I as I = 3/28 04/d.
3.67. q1 = —q (1 — x)I1, q2 = —qx/l. Instruction. If the charge
q is imagined to be uniformly spread over the plane passing through
q
5 l ig 1 neo12