Question

Four charges equal to `-Q` are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is
A. (a) `-Q/2(1+2sqrt2)`
B. (b) `Q/4(1+2sqrt2)`
C. (c) `-Q/4(1+2sqrt2)`
D. (d) `Q/2(1+2sqrt2)`

Answer 1

Correct Answer - B
Net field at A should be zero
`sqrt2E_1+E_2=E_3`
`:. (kQxxsqrt2)/(a^2)+(kQ)/(sqrt2a)^2=(kq)/(a/sqrt2)^2`

`implies(Qsqrt2)/(1)+Q/2=2qimpliesq=Q/4(2sqrt2+1)`