If  then y satisfies

Since, the proton is moving against the direction of electric field so, work is done by the proton against electric field. It implies that electric field does negative work on the proton.
Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

When charge is at , then its potential energy is

Where charge is at , then

Hence, change in potential energy

Potential difference between two equipotential surfaces A and B.



Or

Or
Similarly,
Since,
therefore

In Ist case, when charge is situated at C

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

The electric potential on the surface of shell

Or

Work is required to set up the four charge configuration

The points S and R are inside the uniform electric field, so these will be at equal potential.

When a positive charge is moved from one point to another in an electric of magnetic field, then under the influence of the field force acts on the particle and an external agent will have to do work against this force. But in the given case the charge moves under influence of no field, hence it does not experience any force therefore, no work is done.

Here total electrostatic potential energy is zero

On solving,

At each point on the surface of a conducting sphere the potential is equal.
So,

Electric field

For I region, =constant



For II region,


For III region.
=constant


For IV region,

From these values, we have