Why Electric Field inside a Conductor is Zero?

In this post we will discuss, why electric field inside a conductor is zero. This is very basic but important concept to understand. So we will start will zero and will move further to explain this. Let us assume that a conductor is kept in an external uniform electric field E. The direction of electric field E is shown in the figure.

Before starting the discussion, there are two points to know.

1)      Negative charge move in the direction opposite to the direction of electric field.

2)      Positive charge move in the direction of electric field.

As we know that, a conductor has a lot of mobile or free electrons, therefore when keep the conductor in an external electric field, electrons will experience a force in the direction opposite to the direction of electric field E and will start accumulating at surface A of the conductor. As electrons are moving opposite to the direction of Electric Field E, positive charge will start building at the opposite face B of the conductor. This accumulation of charge on both surface of conductor A and B, will lead to development of Electric Field E� inside the conductor and this developed electric field E� will oppose the flow of further electron toward face A. As the accumulation of electrons increases on the face A, the strength of electric field E� inside the conductor will also increase and will oppose the flow of electron more strongly. But as soon as the strength of developed electric field becomes equal to the strength of external electric field E, no net electric filed will be there inside the conductor to drive the electrons and hence further accumulation of electrons will stop.

Therefore at equilibrium,

Developed Field E� = External Field E

Therefore, net force on electrons = 0 and hence no movement of electrons.

Thus we see that at equilibrium, the strength of electric field inside the conductor is zero.