Along the x-axis, three charges `q/2` , -q and `q/2` and are placed at x = 0 ,x = a and x = 2a respectively. The resultant electric potential at a point P located at a distance r from the Charge `-q (a lt lt r)` is (`epsilon_(0)` is the permittivity of free space).

Options

A. `qa/4pi epsilon_(0)r^(2)`
B. `qa^(2)/4pi epsilon_(0)r^(3)`
C. `q(a^(2)/4)/4pi epsilon_(0)r^(3)`
D. `q/4pi epsilon_(0)r`

Answer

(b)

Explanation

Electric potential due to charges q/2 , -q and q/2 is,
`V = 1/ 4 pi epsilon_(0) q/2(r + a) + 1/ 4 pi epsilon_(0) -q/r + 1/ 4 pi epsilon_(0) q/2(r - a)`
=`1/ 4 pi epsilon_(0) q/2[1/(r + a) - 2/r + 1 / r - a]`