A charge Q is place at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then `Q//q` equals:

Options

A. `Q = sqrt(2)q`
B. `Q = -2sqrt(2)q`
C. `Q = -sqrt(2)q`
D. `Q = 2sqrt(2)q`

Answer

B

Explanation

Let a be the sides of the square.
`F_(1) = F_(2) = (Qq)/(4pi epsilon_(0)a^(2))`
`F_(3) = (Q Q)/(4pi epsilon_(0)(asqrt(2))^(2)) = (Q^(2))/(4pi epsilon_(0)(asqrt(2))^(2))`
As the resultant force on Q is zero, therefore `F_(3) cos 45^(@) = -F_(1)`
`(Q^(2))/(4pi epsilon_(0)(asqrt(2))^(2)) (1)/(sqrt(2)) = -(Qq)/(4pi epsilon_(0)a^(2))` or `Q = -2sqrt(2) q`