Question

Select True or False for the following statements about conductors in electrostatic equilibrium.
Charges prefer to be uniformly distributed throughout the volume of a conductor.
The electric field inside the conducting material is always zero.
All points of a conductor are at the same potential.
Just outside the surface of a conductor, the electric field is always zero.

Answer 1

Concepts and reason

The concept used to solve this problem is conductor in static equilibrium.

Use the gauss’s law to find the position of the net charge on the conductor.

Use the concepts of electric field to find the electric field inside the conductor.

Use the potential and electric field relation to find the point on a surface of a conductor in electrostatic is at the same potential.

Fundamentals

Expression for the charge is,

Here, is the charge, is the surface charge density, and A is the surface area.

Gauss law states that the total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.

Expression for the electric flux is,

Here, is the electric flux and is the permittivity.

Expression for the integral form of gauss law is,

Here, E is the electric field and is the differential area.

Expression for the potential difference is,

Here, is the potential difference and is the differential length.

From the gauss law,

Choose Gaussian surface that everywhere lies just inside the conductor surface.

The electric field is zero everywhere on the Gaussian surface so that the flux is also zero over the surface.

Hence, there can be no internal net charge.

Therefore, this statement is false.

Suppose consider that the there was an electric field inside the conductor inside the conductor.

This results free charges inside the conductor to move and hence this is contradicting to the assumption that they are in electrostatic equilibrium.

At the instant external field is applied to the conductor, the free electrons, initially uniformly distributed, migrate under the influence of the electric field and produces their own electric field that would cancel the external field.

Hence, this statement is true.

Expression for the potential difference is,

From the above equations, the electric field is everywhere perpendicular to the conductor surface.

The line integral is confined to the surface, then the two vectors are always perpendicular to each other and for any points on the surface.

Hence, this statement is true.

Expression for the charge is,

Here, is the charge, is the surface charge density, and A is the surface area.

Expression for the integral form of gauss law is,

Substitute for Q.

Rearrange the above equation to get the electric field,

The electric filed must lie perpendicular to the surface everywhere.

The electric field is only constant in magnitude is uniform over the conductor surface.

Hence, this statement is false.

Ans:

The charges prefer to be uniformly distributed throughout the volume of a conductor is false.