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Homework Statement
Find the electric field due to a rectangular plate with charge Q, length L, width W, at a distance s<< L perpendicular to the plate. The point at that location is exactly above (with respect to the plate) the center of mass of the rectangular plate
Homework Equations
Electric Field due to a rod: E = k q/[r*sqrt(r^2 + (L/2)^2)]
q is the charge of the rod.
r is the distance from the c.m. of the rod to the required location
L is the length of the rod
The Attempt at a Solution
Divide the plate into infinite amount of rods of length L and width dx, and charge dq. Use above equation to represent the electric field due to one of these rods and then integrate over the surface.
r^2 = x^2 + s^2. Unfortunately, I can't state that r rounds to x, because x could even be smaller than s.
The components of the electric field due to the plate that are parallel to it cancel out. So only the components up survive.
dq = dxQ/W. Now I would have to that integral which looks hard to do. My belief is that there must be an easier way to solve this. Is there?
Thank you.