Boundary Conditions for an Infinite Conducting Sheet

AI Thread Summary
Placing an infinite conducting sheet in free space and fixing its potential to φ0 raises challenges in defining boundary conditions due to the potential's behavior at infinity. Despite the potential blowing up at infinity, this does not pose a physical problem, as infinite conducting sheets do not exist in reality. To mathematically address the situation, Gauss's law is applied using a Gaussian pillbox that straddles the surface of the sheet. This approach circumvents the need for boundary conditions typically required in electric potential problems. Ultimately, the solution focuses on the application of Gauss's law rather than traditional boundary problem formulations.
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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.
 
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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).
 
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