Boundary Conditions for an Infinite Conducting Sheet

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SUMMARY

The discussion focuses on solving the potential around an infinite conducting sheet fixed at a potential \varphi_0 in free space. It establishes that while the potential diverges at infinity, this does not pose a physical issue since infinite conducting sheets do not exist in reality. The mathematical solution involves applying Gauss's law using a Gaussian pillbox that intersects the conducting surface, rather than treating it as a conventional electric potential boundary problem.

PREREQUISITES
  • Understanding of Gauss's law in electrostatics
  • Familiarity with electric potential concepts
  • Knowledge of boundary value problems in physics
  • Basic principles of electrostatics and conductors
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  • Study Gauss's law applications in electrostatics
  • Research boundary value problems in electromagnetic theory
  • Explore the concept of electric potential and its mathematical formulations
  • Investigate the physical implications of idealized models in physics
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Physicists, electrical engineers, and students studying electromagnetism who seek to deepen their understanding of boundary conditions and potential theory in electrostatics.

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If we place an infinite conducting sheet in free space, and fix its potential to [itex]\varphi_0[/itex], 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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