Question

Consider a charge Q distance d away from a grounded metal. (“Grounded” means that the electric potential is zero.) The metal has a planar surface at x = 0. Explain qualitatively why the charge Q experiences an attractive force towards the metal for both Q > 0 and Q < 0. (b) Let’s calculate the force on charge Q. There are two so-called “boundary conditions” for the potential: the potential at the metal surface (plane at x = 0) is zero, and the potential far away from the metal (x2 + y2 + z2 ≫ d2) is also zero. Consider the two charges of opposite sign. Show that the potential created by these two charges satisfies the two boundary conditions.

          Consider a charge Q distance d away from a grounded metal.
(“Grounded” means that the electric potential is zero.) The metal has a planar
surface at x = 0. Explain qualitatively why the charge Q experiences an attractive
force towards the metal for both Q > 0 and Q < 0.
(b) Let’s calculate the force on charge Q. There are two so-called “boundary conditions” for the potential: the potential at the metal surface (plane at x = 0) is
zero, and the potential far away from the metal (x2 + y2 + z2 ≫ d2) is also zero.
Consider the two charges of opposite sign. Show that the potential created by these
two charges satisfies the two boundary conditions.

Added by Andrea W.

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