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**Unformatted text preview: **23.46: a) E x = - kQ a 2 + x 2 + a ln 2a a 2 + x 2 - a kQ 2 2 2 2 Ex = - x ln( a + x + a ) - x ln( a + x - a) 2a V =- x x x(a 2 + x 2 ) -1 2 x(a 2 + x 2 ) -1/ 2 kQ - 2 = 2 2 2 a + x - a x a2 + x2 a +x +a (2a ) 1 Ex = = . 2 2 20 x 1 + x 2 a 2 4 0 xa 1 + x a kQ =- 2a b)The potential was evaluated at y and z equal to zero, and thus shows no dependence on them. However, the electric field depends upon the derivative of the potential and the potential could still have a functional dependence on the variables y and z, and hence E y and E z may be non-zero. ...

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