15_6_14B - Thus Ik = The contribution to the total flux...

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Unformatted text preview: Thus Ik = The contribution to the total flux from the pair of surfaces z = 1 and z = 2 of the cube is 2m I2 - m I1 1 1 1 = m tan-1 - 2 tan-1 + tan-1 3 3 2 6 4 1 2 - tan-1 + 2 tan-1 - tan-1 . 3 6 3 2a , and 1 - a2 1 tan-1 a = - tan-1 , 2 a 3 4 1 = - tan-1 = - + tan-1 3 4 2 3 1 2 12 = tan-1 = - tan-1 . 2 6 6 2 6 1 4 2 tan-1 - 2 tan-1 k k 8 + k2 k 5 + k2 1 . + tan-1 k 2 + k2 Using the identities 2 tan-1 a = tan-1 we calculate - 2 tan-1 2 tan-1 Thus the net flux out of the pair of opposite faces is 0. By symmetry this holds for each pair, and the total flux out of the cube is 0. (You were warned this would be a difficult calculation!) ...
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