An electric charge $10^{-3} \mu C$ is placed at the origin $(0,0)$ of X-Y co-ordinate system. Two points A and B are situated at $(\sqrt{2}, \sqrt{2})$ and $(2,0)$ respectively. The potential difference between the points A and B will be

JEE Main · 2007 · 29 Apr 2007 · Offline · Electrostatics

An electric charge

1 0^{- 3} μ C

is placed at the origin

(0, 0)

of X-Y co-ordinate system. Two points A and B are situated at

(2, 2)

and

(2, 0)

respectively. The potential difference between the points A and B will be

(A)9 volt
(B)zero✓ Correct
(C)2 volt
(D)4.5 volt

Answer: (B)

Solution

The potential of a point charge falls off as

V = \frac{k q}{r}

, so it depends only on the distance from the charge. Point A at

(2, 2)

lies at

r_{A} = 2 + 2 = 2

from the origin, and point B at

(2, 0)

lies at

r_{B} = 2

as well. Since both points are the same distance from the charge sitting at the origin, they are at equal potential, and the potential difference between them works out to zero.

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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