Electric Potential Homework: Infinite Wire & Distance R

[chaoseverlasting]

Homework Statement

There is an infinite conducting charged metallic wire. What will the potential at a distance r from the wire be?

The Attempt at a Solution

I know that $$E=\frac{\lambda}{2\pi \epsilon r}$$ and $$E=\frac{-dv}{dr}$$.

Integrating the expression for the electric field wrt r, $$V(r)=-\frac{\lambda}{2\pi \epsilon} logr$$

This, however, isn't the answer. Why?

 

[Mentz114]

You should be integrating the field from an element of the wire from -inf to +inf.

 

[chaoseverlasting]

Ouch. That would make it undefined at that point, right?

 

[Mentz114]

Assume you have linear charge density r, so the charge of a line element is r.dl. The electric field at point r is k.r.dl/(r^2+l^2).

 

[chaoseverlasting]

I can figure out the expression for the electric field, but its the potential I had the question about. Wont it be undefined?

 

[Mentz114]

Rats, I misread the question. Integrating the potential of a line element blows up because it's a scalar. It really does look as if there's nothing you can differentiate to give the 1/r dependence.