A positive point charge is placed near 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 negative point charge of equal magnitude in the mirror image position behind the initial position of the plane.
1 Answer
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This is sort of correct. It is an application of the method of images. Basically the solution to the field equations that meets the boundary conditions is unique. So any way that you can meet these conditions provides a valid solution to the problem (the valid solution). Proving this may be difficult but using it is pretty easy. Keep in mind that the solution is meaningless in the space "behind" this conducting plane but we don't really care.
Now, as for your instructor's statement. If the charge is closer to the "large" plate than the characteristic length of the plate this is a good approximation to the field away from the edges. This same approach is used to get the field in a parallel plate capacitor. Strictly speaking the two configurations are not equivalent. But as an approximation, for the conditions described above, it should be okay.
The method of images will give the exact solution for an infinite plane.