Electric field derivation question

AI Thread Summary
The discussion focuses on deriving expressions for the electric field generated by an infinitely long sheet of charge with surface charge density n. For a point outside the sheet, the electric field E can be expressed as E = λ/(2πε0*(d+L/2)), where λ is the linear charge density related to n by λ = n*L. Additionally, the electric field at a point on the z-axis, a distance z=a above the center of the plane, is given by E = λ/(4πε0*(z+L/2)). The problem was challenging for many students, prompting the professor to allow submissions for extra credit. The key relationships between surface charge density and linear charge density are crucial for solving the problem.
afromanbob
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Hey, if someone can show me the solution to this I'd be very thankful. Here's the question:

An infinitely long sheet of charge has width L and surface charge density n. The sheet lies in the xy-plane between x=-L/2 and x=+L/2

a) Derive an expression for the electric field E along the x-axis for a point outside the sheet a distance d away from the edge of the sheet (the distance from the origin to the point is x=d+L/2)
Hint: How does n relate to the linear charge density, lambda, of a narrow strip of the sheet?

b) Derive an expression for the electric field E at a point on the z-axis a distance z=a above the center of the plane.Thanks.

By the way, I basically have no starting work of mine to show, I'm really quite stumped by this problem. It was actually a question on our test that almost everyone in the class missed, so the professor is allowing us to turn in a solution for a few more points added to our test score. I don't even really understand if the shape described is basically a line... or what...
 
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a) The linear charge density, λ, of a narrow strip of the sheet is related to the surface charge density, n, by λ = n*L. The electric field at the point outside the sheet, a distance d away from the edge of the sheet would then be given by E = λ/(2πε0*(d+L/2))b) The electric field at a point on the z-axis a distance z=a above the center of the plane is given by E = λ/(4πε0*(z+L/2))
 
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