point charge in a conducting plane

[sami23]

Point charge +Q is placed close to a very large conducting plane. A professor of physics asserted that the field caused by this configuration is the same as would be obtained by removing the plane and placing a point charge -Q of equal magnitude in the mirror-image position behind the initial position of the plane. Is this correct? Why or why not?

[betel]

It is correct. The method of placing mirror charges is an easy way to solve such problems.
Experience tells you were to put the charges.
The mathematical way to see this, is by solving the Poisson equation using the correct boundary conditions for the Green function.

[thedore]

It is correct. The method of placing mirror charges is an easy way to solve such problems.
Experience tells you were to put the charges.
The mathematical way to see this, is by solving the Poisson equation using the correct boundary conditions for the Green function.


Does the voltage of the plane matter?

[betel]

Does the voltage of the plane matter?

What do you mean by voltage? A single plane can not have a voltage, you have to specify in relation to what the voltage is considered. But you can have a charge on the plane.

[netheril96]

Does the voltage of the plane matter?

Yes,the plane must be grounded

And the mathematical principle behind such "cheating" solution is uniqueness theorem (http://en.wikipedia.org/wiki/Uniqueness_theorem).

[Antiphon]

Actually you want to refer to the theory of images. The plane does not have to be grounded but it cannot have a net charge and it must be infinite in size.

The principle is simple. Electric field lines are perpendicular to a conducting plane. If you mirror the charges on two sides of an imaginary plane (reverse the sign of the charges on opposite sides of the plane) the electric field lines will be perpendicular to the imaginary plane. So mirrored charges produce the same field as charges in front of a mirror. That's how "mirroring" gets it's name.