It is required to hold equal charges q in equilibrium at the corners of a square. What charge when placed at the center of the square will do this?

Let place a charge Q at center of square such that Q and q are of opposite sign.AC=2l=BD  or  BO=l2For equilibrium of charge at BFBO=FBD+FBA+FBCcos⁡45∘⇒kQql22=kqq2l2+2kqql212⇒Q=q4(1+22) and  Q should be negative of q .