An electric charge `10^-3muC` is placed at the origin (0, 0) of X-Y co-ordinate system. Two points A and B are situated at `(sqrt2, sqrt2)` and (2, 0) respectively. The potential difference between the points A and B will be

Options

A. 4.5 volt
B. 9 volt
C. zero
D. 2 volt

Answer

C

Explanation

`vec(r )_(1) = sqrt(2) hat(i) + sqrt(2)hat(j)`
`|vec(r )_(1)| = r_(1) = sqrt((sqrt(2))^(2) + (sqrt(2))^(2)) = 2`
`vec(r )_(2) = 2hat(i) + 0 hat(j)` or `|vec(r )_(2)| = r_(2) = 2`
Potential at point A is
`V_(A) = (1q)/(4pi epsilon_(0)r_(1)) = (1)/(4pi epsilon_(0)) (10^(-3) xx 10^(-6))/(2)`
`:. V_(A) - V_(B) = 0`.