Question

If a unit charge is taken from one point to another over an equipotential surface, then
A. work is done on the charge
B. work is done by the charge
C. work done on the charge is constant
D. no work is done

Answer 1

We will apply the concept of equipotential surface and work done in terms of potential and charge to get the correct answer. We know that the flow of charge is always from higher potential to lower potential. A surface with the same electric potential at every point is called equipotential surface.
Formula used: We will use the following formula to find the right answer:-
$W=q({{V}_{A}}-{{V}_{B}})$.

Complete step by step solution:
We consider a unit charge, $q$ is taken from point $A$ with potential ${{V}_{A}}$ to the point $B$ with potential ${{V}_{B}}$ over an equipotential surface. Then the work done,$W$ in moving the the unit charge is given as follows:-
$W=q({{V}_{A}}-{{V}_{B}})$………………. $(i)$
But we know that equipotential surface is defined as the surface at which every point has the same electric potential.
That is${{V}_{A}}={{V}_{B}}$………$(ii)$
Putting $(ii)$in$(i)$we get
$W=q({{V}_{A}}-{{V}_{A}})$
$W=q\times 0$
$W=0J$

Hence, no work is done and option $(D)$ is correct.

Additional Information:
Some properties of equipotential surface are as follows:-
$(i)$Two equipotential surfaces can never intersect each other.
$(ii)$Electric field and equipotential surface are always perpendicular to each other.
$(iii)$No work is done in moving a charge from one point to another over the equipotential surface.
$(iv)$If the points in an electric field have the same potential then these points are termed as equipotential points.

Note:
We should keep in mind that every point on an equipotential surface has the same potential and hence, no work is required to move a charge from one point to another. It should also be noted that the shape of the equipotential surface for a point charge is concentric circles. We should also note that for a uniform electric field, any plane perpendicular to the field direction is called equipotential surface.