Boundary Conditions for an Infinite Conducting Sheet

[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.

 

[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).