Let y0 y0 1 2 2 x x0 2 y2 x x0 y0 0 this is an easy

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Unformatted text preview: s is an easy function to plot for various combinations of the position of the original line charge (x 0 , y 0 . T ln c) If we integrate over a strip of width z, we find, where we use the integral x0 0 x x 1 2 y 2 dx 1 2 arctan y0 y0 2 0 0 Q 2 dx tan z 0 and the total charge induced on the plane is , as expected. d) Expanding 4 Q 0 dx z 1 x0 y0 ln R2 R2 R2 ln ln x x0 2 y y0 2 x x0 2 y y0 2 x x0 2 y to lowest non-vanishing order in x 0 , y 0 gives xy 16 2 y x 2 0 0 x y2 so xy 4 y x asym 0 2 2 0 0 x y2 This is the quadrupole contribution. y0 2 ln R2 x x0 2 y y...
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