P 7.1 a) R = g1+3g2 24πag1g2 b) σ = 3V0ε0 2a (g1−g2) (g1+3g2) P 7.2 f(r) = − C αr2 , g(r) = 2C. P 7.3 a) ~J = V0g0 L ln 2 ŷ, ~E = V0 L(1+ y L ) ln...

P 7.1 a) R = g1+3g2 24πag1g2 b) σ = 3V0ε0 2a (g1−g2) (g1+3g2) P 7.2 f(r) = − C αr2 , g(r) = 2C. P 7.3 a) ~J = V0g0 L ln 2 ŷ, ~E = V0 L(1+ y L ) ln 2 ŷ b) P = πa2 V 2 0 g0 L ln2 2 ln ( 1 + 2e 3L ) P 7.4 R = ln(z2/z1) gπk P 7.5 I = 4πkV 2 ln( b a )2 , ρ = V r2 ln( b a ) P 7.6 R = π gd ln(1+ d r ) P 7.7 a) I = LV0 ln(a/b) (βg1 + (2π − β)g2) b) R1 = ln(a/b) Lβg1 R2 = ln(a/b) L(2π−β)g2 RT = ln(a/b) L(βg1+(2π−β)g2) P 7.8 a) ∂2V ∂x2 + 1 x+a ∂V ∂x = 0, V (S)− V (S′) = E0a ln(2) b) R = ln(2) g0a , Q = − ε0E0a 2 2 P 7.9 ~J ( r = a, t = ε0 g ) = g ε0 e−1 a3 3r2 P 7.11 R = 1 2πg ( 1 a1 + 1 a2 − 2 L ) P 7.12 a) ~J = V0g1g2 r(g1 ln(c/b)+g2 ln(b/a)) r̂, ~E = { V0g2 r(g1 ln(c/b)+g2 ln(b/a)) r̂ a < r < b V0g1 r(g1 ln(c/b)+g2 ln(b/a)) r̂ b < r < c b) σ(r = a) = 2πLV0g2 (g1 ln(c/b)+g2 ln(b/a)) , σ(r = c) = − 2πLV0g1 (g1 ln(c/b)+g2 ln(b/a)) c) I = 2πLV0g1g2 g1 ln(c/b)+g2 ln(b/a) d) R = 1 2πL ( ln(c/b) g2 + ln(b/a) g1 ) e) RL = 1 2πL ( ln(c/b) g2 + ln(b/a) g1 ) , P = V 2 0 πLg1g2 2(g1 ln(c/b)+g2 ln(b/a))