# Boundary Conditions for an Infinite Conducting Sheet

1. Mar 27, 2012

### shooba

If we place an infinite conducting sheet in free space, and fix its potential to $\varphi_0$, how do we solve solve for the potential on either side of the sheet? Since the potential blows up at infinity, it seems impossible to define boundary conditions.

2. Mar 30, 2012

### chrisbaird

Yes, the potential does blow up at infinity, but this is not a problem with the physics because there are nor infinite conducting sheets in the physical world. To solve the problem mathematically, you would use Gauss's law with a Gaussian pillbox straddling the surface rather than formulate it as a electric potential boundary problem (what would be your boundary, anyways).