I am not able to understand the question, please help

Question

A charge Q is placed at each of the opposite corners of a square .

A charge q is placed at each of the other 2 corners . if net electrical force on Q is 0(zero) . then Q/q equals 

 

1. -2 x √2
2.  -1
3.  1
4.   - 1/(√2) 

Answer 1

So the key to this problem is that the electric field at the point where Q is located is zero. The Efield from the Q in the opposite corner is kQ/r^2=kQ/(sqrt(2)d)^2=kQ/2d^2 (where d is the length of a side of the square). We multiply the d by rad(2) because the length of the diagonal of a square is just rad(2)*(the length of the side) from pythagorean theorem. The E field from Q is pointing 45 degrees north of east (assuming we chose Q to be on the North East corner). So we need the other two charges (of magnitude q) to cancel this out. The Efield from one of the two q's is just kq/d^2 in the North or East, but combined it'll be sqrt(2)k*q/d^2 in the North East. We need those two to E-fields to cancel, so kQ/2d^2+sqrt(2)kq/d^2=0. Q/2=-sqrt(2)*q, so Q/q=-sqrt(2)/2=-1/sqrt(2) which is choice 4