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**1. Homework Statement**

An infinite grounded conducting cylinder without charge is placed inside a uniform electric field E perpendicular to the surface of the cylinder. Find the electric potential outside the cylinder.

**2. Homework Equations**

**3. The Attempt at a Solution**

I know I have to use the general solution for the Laplace equation in cylindrical coordinates and use the boundary conditions to determine the necessary coefficients. However, I have only one condition (the potential on the surface is equal to V), and after elementary calculations I get: [tex]V(r,\phi)=a_{0} + b_{0}lnr + c_{0}r cos\phi + d_{0}\frac{1}{r}cos\phi - E_{0}rcos\phi[/tex]. The boundary condition gives me two equations, but I have 4 coefficients, so I need another boundary condition. I think something has to be assumed about the potential for [tex]r \rightarrow \infty[/tex], but I don't see any sensible assumptions (we can't just assume that it vanishes there?).