HW7 - Physics 3122 Fall 2010 Homework Set 7 Solutions 3.7(b...

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Physics 3122, Fall 2010: Homework Set 7 Solutions. 3.7( b ) V ( r , θ ) = q 4 πε 0 1 [ r 2 2 ra cos θ + a 2 ] 1/ 2 q 4 πε 0 1 [( ra / R ) 2 2 ra cos θ + R 2 ] 1/ 2 E r = q 4 πε 0 ( r a cos θ ) [ r 2 2 ra cos θ + a 2 ] 3/ 2 q 4 πε 0 ( ra 2 / R 2 a cos θ ) [( ra / R ) 2 2 ra cos θ + R 2 ] 3/ 2 E r r = R = q 4 πε 0 ( R a cos θ ) [ R 2 2 Ra cos θ + a 2 ] 3/ 2 q 4 πε 0 ( a 2 / R a cos θ ) [ a 2 2 Ra cos θ + R 2 ] 3/ 2 = q 4 πε 0 ( a 2 R 2 )/ R [ R 2 2 Ra cos θ + a 2 ] 3/ 2 σ = ε 0 E r = q 4 π R ( a 2 R 2 ) [ R 2 2 Ra cos θ + a 2 ] 3/ 2 3.9 E s 2 π sL = λ L / ε 0 E s = λ /2 πε 0 s V = ( λ /2 πε 0 )ln( s ) = ( λ /4 πε 0 )ln( s 2 ) V = λ 4 πε 0 ln[ y 2 + ( z ζ ) 2 ] + λ 4 πε 0 ln[ y 2 + ( z + ζ ) 2 ] = λ 4 πε 0 ln y 2 + ( z ζ ) 2 y 2 + ( z + ζ ) 2 Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ z = 0 V = λ 4 πε 0 ln y 2 + ζ 2 y 2 + ζ 2 Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ = λ 4 πε 0 ln 1 [ ] = 0 E z = V z = λ 4 πε 0 2( z ζ ) [ y 2 + ( z ζ ) 2 ] λ 4 πε 0 2( z + ζ ) [ y 2 + ( z + ζ ) 2 ] σ = ε 0 E z z = 0 = λζ π ( y 2 + ζ 2 ) 3.12 V (0, y ) = V 0 0 y a /2 V 0 a /2 y a Χ੿ Ψએ Ωટ C n
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