problem23_90

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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23.90: For an infinitesimal slice of a finite cylinder, we have the potential: . axis s cylinder' the on 2 ) 2 ( ) 2 ( ) 2 ( ln . where ) ( ) ( ) ( 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 - - + + - + + - = - = + = + - = + - = + - = - - - - x L R x L x L R x L L kQ V z x u R u du L kQ R z x dz L kQ V R z x dz L kQ R z x dQ k dV L L x L x L b) For : R L << - - + + - + + - - - + + - + + - x L R xL x x L R xL x L kQ x L R x L x L R x L kQ V 2 2 ln 2 ) 2 ( 2 ) 2 L ( ln 2 2 2 2 2 2 2 2 + - - + + + + - + + - 2 2 2 2 2 2 2 2 ) 2 ( ) ( 1 ) 2 ( 1 ln x R x L x R xL x R x L ) x (R xL L kQ V + - - + + + + - + + - 2 2 2 2 2 2 2 2 ) 2 ( ) ( 2 1 ) 2 ( ) ( 2 1 ln x R x L x R xL x R x L x R xL L kQ V + - - + + =
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