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# HW9 - Physics 3122 Fall 2010 Homework Set 9 Solutions 3.27...

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Unformatted text preview: Physics 3122, Fall 2010: Homework Set 9 Solutions. 3.27 Q = 3 q − 2 q − 2 q + q = 0 P = 3 q ( a ˆ z ) + ( − 2 q )( − a ˆ y ) + ( − 2 q )( a ˆ y ) + q ( − a ˆ z ) = 2 qa ˆ z V = Q 4 πε r + p ⋅ ˆ r 4 πε r 2 + = + 2 qa ˆ z ⋅ ˆ r 4 πε r 2 + = qa cos θ 2 πε r 2 + 3.29 V ( r ) = q /4 πε r − ζ ˆ z /2 − q /4 πε r + ζ ˆ z /2 V ( r ) = q /4 πε ( r 2 − r ζ cos θ + ζ 2 /4) 1/ 2 − q /4 πε ( r 2 + r ζ cos θ + ζ 2 /4) 1/ 2 = ( q /4 πε r )[(1 − ζ cos θ / r + ζ 2 /4 r 2 ) − 1/ 2 − (1 + ζ cos θ / r + ζ 2 /4 r 2 ) − 1/ 2 ] (1 − ζ cos θ / r + ζ 2 /4 r 2 ) − 1/ 2 = 1 − 1 2 ( − ζ cos θ / r + ζ 2 /4 r 2 ) + 3 8 ( − ζ cos θ / r + ζ 2 /4 r 2 ) 2 − 5 16 ( − ζ cos θ / r + ζ 2 /4 r 2 ) 3 + = 1 + 1 2 ζ cos θ / r − 1 8 ζ 2 / r 2 + 3 8 ζ 2 cos 2 θ / r 2 − 3 16 ζ 3 cos θ / r 3 + 5 16 ζ 3 cos 3 θ / r 3 + = 1 + 1 2 ζ cos θ / r + 1 8 ζ 2 (3cos 2 θ − 1) / r 2 +...
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HW9 - Physics 3122 Fall 2010 Homework Set 9 Solutions 3.27...

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