Boundary Conditions for an Infinite Conducting Sheet

In summary, to solve for the potential on either side of an infinite conducting sheet with a fixed potential of \varphi_0, one would use Gauss's law with a Gaussian pillbox straddling the surface rather than formulating it as an electric potential boundary problem. The blow up of potential at infinity is not a concern in the physical world as there are no infinite conducting sheets.
  • #1
shooba
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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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  • #2
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).
 

FAQ: Boundary Conditions for an Infinite Conducting Sheet

What is a conducting sheet?

A conducting sheet is a material that allows electric charges to move freely within it, making it a good conductor of electricity. It can be made from various materials such as metals or conductive polymers.

What are boundary conditions for an infinite conducting sheet?

Boundary conditions for an infinite conducting sheet refer to the constraints that must be satisfied at the edges of the sheet in order to accurately model its behavior in an electromagnetic field. These conditions describe the relationship between the electric and magnetic fields at the boundary of the sheet.

Why are boundary conditions important for an infinite conducting sheet?

Boundary conditions are important because they help us understand and predict the behavior of electromagnetic fields near the edges of a conducting sheet. They also allow us to accurately model and analyze complex systems involving conducting sheets, such as antennas or microwave circuits.

What are some common boundary conditions for an infinite conducting sheet?

Some common boundary conditions for an infinite conducting sheet include the electric field being perpendicular to the sheet's surface, and the magnetic field being parallel to the surface. Another common condition is that there is no electric field inside the sheet.

How are boundary conditions for an infinite conducting sheet derived?

Boundary conditions for an infinite conducting sheet are derived from Maxwell's equations, which describe the relationship between electric and magnetic fields in an electromagnetic field. By applying these equations to the edges of the sheet, we can determine the constraints that must be satisfied for the sheet to behave as a perfect conductor.

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