Four point charges `-Q, -q, 2q` and `2Q` are placed, one at each corner of the square. The relation between `Q` and `q` for which the potential at the centre of the square is zero is

Options

A. Q = - q
B. `Q = -(1)/(q)`
C. Q = q
D. `Q = (1)/(q)`

Answer

A

Explanation

Let a be the side length of the square ABCD.
`:. AC = BD = sqrt(a^(2) + a^(2)) = a sqrt(2)`
`OA = OB = OC = OD = (asqrt(2))/(2) = (a)/(sqrt(2))`
Potential is a scalar quantity.
Potential at the centre O due to given charge configuration is
`V = (1)/(4pi epsilon_(0))[((-Q))/(((a)/(sqrt(2)))) + ((-q))/(((a)/(sqrt(2))))+ ((2q))/(((a)/(sqrt(2))))+ ((2Q))/(((a)/(sqrt(2))))] = 0`
`rArr -Q - q + 2q + 2Q = 0` or Q = -q