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Homework Statement
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.
Homework Equations
Gauss' Law
Work Formula
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 energy should depend 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