CONDUCTORS AND ELECTRIC FIELDS

When a conducting material is placed in a uniform
electric field as shown in the figure, free electrons
migrate in a direction opposite to the electric field
and get deposited on one side of the metal surface
while the positive charge gets deposited on the other
side of the conductor. This produces an electric field
inside the conductor and the migration of charges stops when the internal electric field becomes equal to the external field.

If we draw a Gaussian surface inside the conductor as shown in the figure, then since the electric field on it is zero, the net electric charge enclosed by it is also zero.
The important conclusions are:
( 1 ) Stationary electric charge distribution is induced on the surface of the conductor.
( 2 ) Both the electric field and the net electric charge inside the conductor are zero.
( 3 ) At every point on the outer surface of the conductor, the electric field is perpendicular to the surface. This is so because the electric charge on the surface is stationary which means that no tangential force acts on it, thus proving that the electric field on the surface has no tangential component.

Consider another example of a hollow conductor placed in an external electric field. Here also, the electric charges deposit on the outer surfaces and the electric field inside is zero as there is no charge inside. This phenomenon is called Electro-static Shielding. When a car is struck by lightning, the person sitting inside is saved from lightning as the car is hollow and acts like an electrostatic shield. Electric field inside a charged conductor which is NOT in an electric field is also zero. Consider a Gaussian surface close to the surface of the conductor as shown by broken line in the figure. The line integration of the electric field along the Gaussian surface being zero, the net electric charge enclosed by it is also zero. This shows that in a charged conductor, the electric charge gets distributed on the outer surface of the conductor. As the electric charges are stationary, the direction of the electric field will be perpendicular to the surface of the conductor as shown in the figure and its magnitude will be
 σ / Є0 

To explain it, consider a pillbox shaped Gaussian surface on the surface of the conductor as shown in the above figure.

The charge enclosed by the Gaussian surface = A .σ
The total flux passing through this surface = A E
Therefore by Gauss’s law, A E = σ / Є0 
If σ  is not uniform along the surface, its proper value at the point should be used to calculate value of E at that point.
If a positive electric charge is placed in the cavity of the conductor as shown in the adjoining figure, it induces
charges on the inner and outer surfaces of the conductor in such a way that the field will be zero in the interior portion of the conductor.