The diagram below shows a rod of length L and net charge Q (distributed uniformly over its length) oriented parallel to a grounded infinite conducting plane at the distance d from the plane.

(a) Evaluate a double integral to find the exact force exerted on the rod by the plane.
(b) Simplify your answer in part (a) in the limit d>>L. Give a physical argument for your result.
(c) Find the charge density σ(x, y) induced on the conducting plane.
(d) Find the total charge induced on the plane without integrating σ(x, y).

Transcribed Image Text:

X d Q L Z