(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Approximate an infinite field of charge as a sheet of infinitely long charged wires each with charge dQ = λL . Use the formula for the electric field of a wire in the limit as L goes to infinity to derive the formula for an infinite sheet of charge dencity η. You need to express λ in terms of of the surface charge density η times an infinetismall distance.

2. Relevant equations

E of infinite line charge = λ/(4 π e0 r)

integral of x/(x^2+y^2) dy = arctan (y/x)

3. The attempt at a solution

Wow... I don't even know where to start

I'll assume the wires run parallel to the y-axis

then the area of each wire is L*dx (assumign dy is the thickness of each wire

η = Q / A Now the area of each wire is L*dx , and since the charge of each is dQ

η = dQ / L*dx = λL/L*dx = λ/dx

honestly I have no idea what else to do or if there was even a point to doing what i just did...help!

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# Derive electric field of infinite plane from field of infinite line

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