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**1. 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

**2. 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

**3. 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.