Problem 2: (3 pts) A point charge Q is located in air at a height h above a grounded conducting plane. (a) Use the method of images to sketch an equivalent problem for finding the fields above the grounded plane. (b) Find the total induced charge on the plane. (c) What is the electric force on the point charge due to the induced surface charges on the plane?
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In this case, we have a point charge above the ground plane, so we need to introduce a mirror charge below the ground plane. We can place the mirror charge directly below the original charge, at the same distance from the ground plane. The mirror charge will have Show more…
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A charge $Q$ is placed a distance $d$ from a very large conducting plane. What is the electric field at a point $P$ a distance $2 d$ from the plane? (See Figure $3.23 .)$ [Hint: Answer this as follows (the method of images). Draw field lines to convince yourself that the same lines would be obtained if instead of the plane, an equal and opposite charge were placed at a position that is the mirror image of the charge in the plane. Thus, the electric field in the presence of the plane would be the same as the electric field of two equal and opposite charges without the plane. Thus, find this field at point $P .$
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