Question

Equipotentials 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 : This question can be answered by analysing the equipotential surfaces for a point charge. Then we have to appreciate the fact that any collection of charge will be approximately equal to a point charge for infinite distances.

Complete step by step answer
We know that a collection of charges basically forms a charge distribution. Let us suppose that the charge distribution is in the form of a line. For great distances from this linear charge distribution, the length of this will become negligible. So, the linear charge will become equivalent to a point charge when the distance tends to infinity.
We know that the electric field lines for a point charge are directed radially outwards or inwards with the point charge as the centre depending upon whether the charge is positive or negative. We also know that the equipotential surfaces are always perpendicular to the electric field lines. So the equipotential surfaces for a point charge are the spheres centred at the point charge, since the electric field lines are directed along the radial direction.
As the linear charge distribution is equivalent to a point charge for great distances, so the equipotential surfaces for the linear charge distribution will also be spheres.
By the similar argument as above for any kind of charge distribution, we can say that the equipotential surfaces for them also are spheres.
Thus the equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately spheres.
Hence, the correct answer is option A.

Note
We may think the answer to this question to be option B, that is, planes. But the planes are the equipotential surfaces for a region where a uniform electric field is present. But for any finite non zero charge distribution, the electric field is inversely proportional to the distance. So the equipotentials will only be spheres at great distances.