# Earthing a system of parallel plates

our sir has taught us that when in a system of conducting infinite plates kept parallel to each other, when any one of them is earthed, then the charges present on the free ends(i.e. the open sides of the parallel plates at the 2 ends) will become zero!

Say we have 3 infinite conducting parallel plates $A,B,C$ with charges $q_1,q_2,q_3$. Now say that $A$ is earthed. Then we have been told that the charges on free end are zero, and hence a charge of $-(q_2+q_3)$ is induced on the inner face of $A$.

Can anyone please explain why this occurs?

## 1 Answer

It happens to minimize the energy content of the system.

The electric field stores energy in the form of electrostatic potential energy. Remember, you have to do work to bring the system in the state explained in question. This work is stored as energy (1st law of thermodynamics). Earthing opens the path to redistribution of charges so that energy is minimized (2nd law of thermodynamics). Unfortunately, the bound charges can't move, so the free charges move in/out of system to minimize the electric field volume to minimize energy. You can do elementary calculation to find out that the earth takes (q2 + q3) amount of charge from the system.

• Why are the"free charges" free? That is the part I can't understand. – Sidharth May 24 '18 at 15:38
• because the net electrostatic force on them is zero and they are in a conductor, hence free to move around. – shaktimaan May 25 '18 at 3:58