Surface Object Integration

Surface Object Integration - Potential on axis of square...

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Potential on axis of square The Problem: Given a r surface with charge density σ and edge length 2 L , find the electric potential at a point a distance z perpendicularly away from the center of the square. A Solution: Chop & Coordinates Slice plate into many thin rods of length 2 L . Choose x and y axes in the plane of the square and centered on it, with the y axis parallel to the thin rods. That way, the thin rods have width dx . The z axis passes through the point of interest. Contribution An arbitrary rod contributes a potential of 22 ln Ld L Vk λ ⎛⎞ ++ = ⎜⎟ +− ⎝⎠ , where d is the distance perpendicularly from the midpoint of the rod to the point of interest. In this case, d is slanted, connecting a point on the x axis with the point
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