Test: Electrostatics of Conductors

Electric field at A is different from field at B because, E= K/r²​
we know that conductor is an equipotential surface, so potential will be the same at A and B.
As charge density, σ∝1/r​, then charge density is different at A and B.

Electric field at the surfaces of charged conductors is σ/ε0​.n, where n is a unit vector normal to the surface.
We clearly see that the electric field is perpendicular to surface charge density (σ).
 

The electric field is zero inside a conductor Because the net charge inside a conductor remains zero , the total charge of a conductor resides on its surface , as charges want to attain equilibrium so they come on surface , to minimize the  repulsion among them .As the  charge inside a conductor is zero therefore , if we apply Gauss' theorem to find the electric field inside a conductor , we find it zero .

Given that some charge is given to a conductor then the whole charge is distributed over its surface only. Inside the conductor, the electric field is zero whereas potential is the same as on the surface. Hence, throughout the conductor, potential is the same i.e, the whole conductor is equipotential.

Since the electric field inside the conductor is zero and has no tangential component on its surface, therefore, no work is done in moving a test charge within the conductor or on its surface. It means the potential difference between any two points inside or on the surface is zero. Hence, electrostatic potential is constant throughout the volume of the charged conductor and has the same value on its surface as inside it.

On an irregularly shaped conductor, the surface charge density is greatest at the locations where the radius of curvature of the surface is smallest i.e, charge density is inversely proportional to radius of curvature of surface. Since the radius of curvature is least at sharp portion and maximum at flat portion, so, charge density is high at sharp portions and less at flat portions.

When there is potential difference across the conductor, the electric field is set up. Due to this charge will flow across the conductor. But when conductors have the same potential the charge will not flow from one conductor to the other.

If a charge q is placed outside than the electric field lines incident on the conducting sphere , if some charge is developed due to thee lines than opposite surface becomes oppositely charge and the total charge becomes zero