Question

Equipotential at a great distance from a collection of charges whose total sum is not zero are approximately:
(A) Spheres
(B) Planes
(C) Paraboloids
(D) Ellipsoids

Answer 1

Hint if we draw a surface in such a way that the electric potential is the same at all the points of the surface, it is called equipotential surface. The component of the electric field parallel to as the potential does not change in this direction. Thus, the electric field is perpendicular to the equipotential surface. For a point charge, the electric field is radial and the electric field is radial and the equipotential surface are concentric spheres with centers at the charge.

Complete Step by step solution
In this problem, the collection of charges, whose total sum is not zero, with regard to great distance can be considered as a point charge.
Now we know that the electric potential due to point charges $q$ is given by
$V = {k_e}\dfrac{q}{r}$
Since, ${k_e}$ and $q$ are constant
Therefore, we can write
$V\alpha \dfrac{1}{r}$
This suggests that electric potentials due to point charge are the same for all equidistant points. the locus of these equidistant points, which are at same potential, form a sphere surface.
Hence, the equipotential at a great distance from a collection of charges whose total sum is not zero are spheres.

Option (A) is correct.

Note The work done in moving a charge between two points in an equipotential surface is zero. If a point charge is moved from point \[{V_A}\] to ${V_B}$ in an equipotential surface, then the work done in moving the charge is given by
\[W = q({V_A} - {V_B})\]
As \[({V_A} - {V_B})\] is equal to zero, the total work done is $W = 0$ .