problem21_87

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

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Unformatted text preview: 21.87: a) dE = k dq kQ dy kQx dy = with dE x = 2 2 2 ( x + y ) a( x + y ) a( x 2 + y 2 ) 3 2 2 and dE y = - KQy dy . Thus: a( x 2 + y 2 ) 3 2 Ex = 1 Qx dy ( x 2 + y 2 )3 40 a 0 a a 2 = = 1 Qx 1 2 40 a ( x + a 2 )1 2 a 1 Q = 2 2 x 40 x( x + a 2 )1 2 -1 Q ydy Ey = ( x 2 + y 2 )3 40 a 0 -1 Q 1 1 - 2 x ( x + a 2 )1 2 40 a b) Fx = -qE x and Fy = -qE y where E x and E y are given in (a). 2 1 qQ 1 qQ a 2 1 qQa 2 2 -1 2 (1 - (1 + a / x ) ) = . c) For x >> a, Fy = 2 40 ax 40 ax 2 x 40 2 x 3 1 qQ a2 1 + 2 Looks dipole-like in y-direction Fx = - 40 x 2 x Looks point-like along x-direction -1 2 qQ . 40 x 2 ...
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