HW6 - Physics 3122, Fall 2010: Homework Set 6 Solutions....

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Physics 3122, Fall 2010: Homework Set 6 Solutions. 3.4 r r E 1 = ρ / ε 0 r r E 2 = / 0 r E = r E 1 r E 2 r r E = 0 V r E d r a S = r ( V r E ) d τ Γ = V r r E d Γ + r E r Vd Γ = ( r E ) 2 d Γ V 1 = V 2 on S V = V 1 V 2 = 0 on S ( r E ) 2 dt Γ = V r E d r a = 0 S V 1 / n = V 2 / n on S V / n = 0 on S ( r E ) 2 dt Γ = V r E d r a S = V ( V / n ) da = 0 S 3.6 Charges: q at 3 s 2 q at s Images: 2 q at s q at 3 s F q = 2 q 2 4 πε 0 (2 s ) 2 + 2 q 2 4 0 (4 s ) 2 + q 2 4 0 (6 s ) 2 = 29 72 q 2 4 0 s 2 3.8 V = 1 4 0 q ( r 2 2 ra cos θ + a 2 ) 1/2 q ( r 2 a 2 / R 2 2 ra cos + R 2 ) 1/2 + q 0 r V r = R = q 0 4 0 R = V 0 q 0 = q = qR / a F = qq 0 4 0 a 2 + q q 4 0 ( a b ) 2 = q 2 R / a 4 0 1 a 2 1 ( a R 2 / a ) 2 = q 2 R 4 0 a 1 a 2 a 2 ( a 2 R 2 ) 2 = q 2 R 4 0 a a 4 2 a 2 R 2 + R 4 a 4 a 2 ( a 2 R 2 ) 2 = q 2 R 3 4 0 a 3 ( R 2 2 a 2 ) ( a 2 R 2 ) 2 3.10 Charge: q at a ˆ x + b ˆ y Images: q at a ˆ x + b ˆ y , q at a ˆ x b ˆ y , q at a ˆ x b ˆ y V = q 4 0 [( x a ) 2 +
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