3.105. C = 4asoa/In (R2/R1).
3.106. When siR iElm = 82R2E2m.•
3.107. V =
[ln (R2/R1)
(81/ 82) In (R3/R2)1
3.108. C
2T80 In (b/ a).
3.109. C
2Itso/ln (2b1a).
3.110. C z 2neosa. Instruction. When b >> a, the charges can
be assumed to be distributed practically uniformly over the surfaces of the balls.
3.111. C
4asoa.
3.112. (a) Ctotal
Cl C2 + C3; (b) Ctotai = C.
3.113. (a) C = 2s0S/3d; (b) C = 380S/2d.
3.114. V
V1 (1
Ci/C 2) = 9 kV.
3.115. U = 61(1 + 3rd + 12) = 10 V.
3.116. C x = C (11/5 — 1)/2 = 0.62C. Since the chain is infinite,
all the links beginning with the second can be replaced by the capacitance Cx equal to the sought one.
3.117. V1 = q/C1 = 10 V,
V2 = q/C2 = 5
cpB + 6) C1C2I(C1 + C2).
V 1 = (62— 60/(1 + C11C2), V2 =(6., — 62)41 + c2/c1).
q = 61 — 621 c1c2/(c1 + C2).
c2cs—cic4
TA — TB=
(C 1 C2) (C3+c4)
In the ease when C1 /C2=
V
3.121. q0.06 mC.
— 1/C1 1/C2 1/C3_
3.122. q1 = gC2, q2= — gUtC2/(Ci -FC2)•
3.123. q1 - = 6C1 (C1 — C2)/(C1
= — 24 .tC,
42= gC2 (C1 — C2)/(C1 + C2) — 36 I.LC, q3 = 6 (C2— C1) = + 6011C.
3.124. WA— TB (C2g2—Cigi)/(C1 1- C2+ CO3.125. (pi =
W2C2 + W1C3+ W1 (C2+ CS)
ci d-c,-Fc3
W3c3— W2 (C1+ C3)
W1 C1W2C2 -43 (C1+ C2)
(4)2 =
C1+C2±C3
,
W3
Ci+C2±C3
3.126. Ct otal =
2C1C2 +C3 (C1 +C2)
ci+C2+2c3
q2143180a.
21n 2 q 2
4:180 a •
—q2/85t80 /.
41q 2/4aso /.
= — 1/2172C1C2/(C1 + C2) =
e2cco/(2c +
1/2ce22. It is remarkable
61.
W2 +
V, where q =
= (WA —
3.118.
3.119.
3.120.
C3/C4.
3.127. (a) W = (4/- -P 4) q2/4neoa;
(b) W=(1/2-4) = 2
q2/43teoa;
(c) W= — 172
3.128. W —
3.129. W =
3.130. W =
3.131. AW
3.132. Q =
3.133. Q =
independent of
3.134. W =
1
q?
4n60 \ 2R1
4_ q2
q1q2
2R2
R2
•
that the result obtained is
—0.03 mJ.
312