3.105. C = 4asoa/In (R 2 /R 1 ).
3.106. When siRiElm = 8 2R2E2m.•3.107. V = (^) [ln (R2/R1) ( 8 1/ 8 2) In (R3/R2)1
3.108. C 2T8 0 In (b/ a).
3.109. C 2Itso /ln (2b1a).
3.110. C z 2neo sa. Instruction. When b >> a, the charges can
be assumed to be distributed practically uniformly over the sur-
faces of the balls.
3.111. C 4asoa.
3.112. (a) Ctotal Cl C2 + C3; (b) Ctotai = C.
3.113. (a) C = 2s 0 S/3d; (b) C = 38 0 S/2d.
3.114. V V 1 (1 Ci/C^2 ) = 9 kV.
3.115. U = 61(1 + 3rd + 1^2 ) = 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 ca-
pacitance Cx equal to the sought one.
3.117. V 1 = q/C 1 = 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 C 2 ) (C3+c4) In the ease when C1/C2=
V
3.121. q-—1/C 1 1/C 2 1/C 3 0.06 mC.
3.122. q (^1) = gC2, q2= — gUtC2/(Ci -FC2)•
3.123. q 1 - = 6C (C 1 1 — C 2 )/(C^1 = — 24 .tC,
42= gC2 (C1— C2)/(C1 + C2) — 36 I.LC, q^3 =^6 (C2— C1) = +6011C.
3.124. WA— TB (C2g2—Cigi)/(C1 1- C2+ CO-
3.125. (pi = W2C2 + W1C3ci d-c,-Fc+W1 (C2+ CS) 3
W3c3— W2 (C1+ C3) W1 C1W2C2-43 (C1+ C2)
( 4 )2 = (^) C1+C2±C3 , W3 (^) Ci+C2±C3
3.126. Ctotal = 2C1C2 +C3 (C1 +C2)
ci+C2+2c3
q 2143180 a.
21n 2 q 2
4:18 0 a •
—q 2 /85t8^0 /.
41 q^2 /4aso/.
= — 1 /2 172 C1C2/(C1 + C2) =
e2cco/(2c +
1/ 2 ce2 2. It is remarkable
61.
W2 +
V, where q =
= (WA —
3.118.
3.119.
3.120.
C 3 /C 4.
3.127. (a) W = (4/- -P 4) q 2 /4neoa; (b) W=(1/2-4) = 2 q 2 /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 \ 2R 1
4 q2^ q1q2
2R2 (^) R2 •
that the result obtained is
—0.03 mJ.
312