Question

How do I solve this question?

Answer 1

(D) Decrease then increase is the answer.

Explanation:

Symmetry of the problem (charges at A and B are identical) rules out the continuous increase/decrease options. Because continuous increase / decrease means potential at one end is higher/lower than the other. How can that be if both charges are identical?

So it is either Increase then decrease or Decrease then increases. Which of this is correct?

Remember, Electric field is the negative of potential gradient. This indicates the fact that electric field is directed along the direction of decreasing potential.

If you take a test charge `q_0` and move it from A to B :

• Close to A, the effect of A on the test charge is dominant and it experiences a net repulsive force toward B. This means the electric field is directed towards B. So that is the direction of decreasing potential. So we conclude that the potential decreases as we start moving towards B.
• At the midpoint connecting A and B, the test charge experiences no force because the repulsive force of A is exactly cancelled by the repulsive force of B. This is the point of minimum potential and the electric field here is zero.
• Once you start moving further towards B the effect of B starts dominating. The test charge now starts experiencing a net repulsive force towards A. So the the electric field now turns its direction and starts pointing towards A. So the direction from B to A is the direction of decreasing potential. But we are moving towards B. So the potential starts increasing again as we get closer to B.