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. `1`
B. `-1/sqrt(2)`
C. `-2sqrt(2)`
D. `-1`

Answer

C

Explanation

Here `vec(F)_(1)+vec(F)_(2)+vec(F)_(3)=0` …(i)
`|vec(F)_(1)+vec(F)_(2)|=(sqrt(2)KQ^(2))/a^(2)`
`|vec(F)_(3)|=(KQ^(2))/((sqrt(2)a)^(2))`
from (i)
`(sqrt(2)KQq)/a^(2)+(KQ^(2))/((sqrt(2)a)^(2))=0`
`(sqrt(2)KQq)/a^(2)=(KQ^(2))/(2a^(2))rArr Q=-2sqrt(2) q`