Potential on axis of square The Problem: Given a r surface with charge density σand edge length 2L, find the electric potential at a point a distance zperpendicularly away from the center of the square.A Solution: Chop & Coordinates Slice plate into many thin rods of length 2L. Choose xand yaxes in the plane of the square and centered on it, with the yaxis parallel to the thin rods. That way, the thin rods have width dx. The zaxis passes through the point of interest. Contribution An arbitrary rod contributes a potential of 22lnLd LVkλ⎛⎞++=⎜⎟+−⎝⎠, where dis the distance perpendicularly from the midpoint of the rod to the point of interest. In this case, dis slanted, connecting a point on the xaxis with the point
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