Electrostatic Potential- An IIT-JEE 2007 MCQ

The following MCQ which appeared in IIT-JEE 2007 question paper is meant for checking whether you have the correct idea about electric potential and potential difference:

Positive and negative point charges of equal magnitude are kept at (0,0, α/2) and(0,0,–α/2), respectively. The work done by the electric field when another positive point charge is moved from (–α,0,0) to (0,α,0) is

(a) positive

(b) negative

(c) zero

(d) depends on the path connecting the initial and final positions

You should have a three dimensional mental view of the Cartesian coordinate system to work out this problem in no time. Even without drawing a figure, some of you will be able to work this out. But you may draw a quick figure to help you.

In the figure shown, the positions of the equal positive and negative charges and the movement of the third positive charge from P to Q are indicated. The path shown is straight, but it can be any curve, since the work done is independent of the path in an electrostatic field and is dependent on the initial and final positions only.

Since P and Q are equidistant from the positive and negative charges, the resultant potentials at P as well as Q due to these charges is zero. Therefore, no work need be done for moving the third charge from P to Q [Option (c)].