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

This isn't a real HW problem for me but just a question I asked myself and I am slightly confused by the solution I get. Here is the situation. You have an infinite line charge and a point charge q. Find the potential energy given to the point charge from the infinite line charge.

2. Relevant equations

Gauss' Law

Work Formula

3. The attempt at a solution

Here is my solution.

∫E*dS = Q/ε

Q=∫Q'*dL where Q' is charge per length integrated from 0 to L

Q = (Q')L

∫E*dS = E*2∏rL

E*2∏rL = (Q')L/ε

E = Q'/(2∏rε)

We know that F = qE so

F= qE = (q*Q')/(2∏rε)

Work done on a point particle to move it from the line charge to a distance r would be

W = F*r = (q*Q')/(2∏ε)

So my final answer is

Potential Energy = (q*Q')/(2∏ε)

My math certainly leads up to this answer but I am finding it slightly difficult to accept. I just feel that the potential energyshoulddepend on the distance from the line charge to the point charge but this equation says otherwise. Am I doing something wrong or is my math right???

Thanks

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# Potential Energy from an infinite line charge

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