Electric field derivation question

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SUMMARY

The discussion focuses on deriving expressions for the electric field generated by an infinitely long sheet of charge with surface charge density n and width L. For a point outside the sheet at a distance d from its edge, the electric field E is calculated using the formula E = λ/(2πε0*(d+L/2)), where λ is the linear charge density defined as λ = n*L. Additionally, the electric field at a point on the z-axis, a distance z=a above the center of the sheet, is expressed as E = λ/(4πε0*(z+L/2)). These derivations clarify the relationship between surface charge density and linear charge density.

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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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