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Problem

A point charge is placed  at a distance \(d\) from an infinite grounded
conducting plane sheet. Assuming the standard image charge, find

1. induced surface charge density. Show that the total induced charge is equal to−q
2. find the potential due to the induced charge;
3. using Coulomb's law, find the force between the charge and conducting sheet making use of the induced surface charge density on the plane.

\(\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\)

Problem:
What is the electrostatic energy of a point charge placed near an grounded infinite conducting plane. Show that this is not equal to the energy of the point charge and it image.

Two point charges \(Q\) and \(Q^\prime\) are located at positions given by \(\vec{a}, \vec{b},  (a\ne b) \). Find the conditions on \(Q, Q^\prime, a, b \)  so that the potential on the surface of a sphere of radius \(R\) with center at the origin may be zero.

Note the result of this problem is used in solution for electric potential of a grounded conducting sphere in presence of a point charge by the method of images.

This is a repository of NOTES in EM-Theory.
Recommended only for authors and content developers.
Not useful for visitors looking for study material.

The concept of electric field to describe the interaction of charged particles is briefly explained. Instead of the Coulomb interaction, which is an instantaneous action, we say a charge produces electric field which in turn acts on another charge  present at some other point. Similarly the magnetic force on a current, or a moving charged particle is described in terms of magnetic field produced by a magnet or a current..

The Si system of units are explained. This is the system that will be used everywhere in the resources of Proofs program.