problem23_64

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

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23.64: a) From Example 23.12: 1 1 ln 2 ln 2 ) ( 2 2 2 2 2 2 2 2 - + + + = - + + + = x a x a x a x a a kQ a x a a x a a kQ x V . 2 2 2 1 2 1 2 ) ( 2 1 ) 1 ( ln and , 1 2 1 1 1 , If 2 2 2 2 2 2 x kQ x a a kQ x a x a x a x a a kQ x V α α α x a x a x a x a x a x a = = + + - - + + + + + + ± + ± + << That is, the finite rod acts like a point charge when you are a long way from it. b) From Example 23.12: . 1 1 1 1 ln 2 ln 2 ) ( 2 2 2 2 2 2 2 2 - + + + = - + + + = a x a x a kQ a x a a x a a kQ x V ). / 2 ( ln 2 λ ) 2 ln( 4 ) 2 ( In 1 4 ln 2 ) 2 ( ) 2 2 ( ln 2 ) ( 2 1 ) 1 ( ln and , 2 1 1 1 1 1 , 0 0 2 2 2 2 2 2 2 2 2 2 x a πε
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Unformatted text preview: x a a πε Q x a a kQ x a a kQ a x a x a kQ x V α α α a x a x a x If = = ≈ + = + ≈ ⇒ ⋅ ⋅ ⋅ + + ≈ + + ± ≈ ± + << Thus , 2 and , 2 λ a R a Q = ≡ which is the only natural length in the problem....
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