Four point charges -Q,-q, 2 q and 2 Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

Step-by-step solution

Let a be the side length of the square A B C D . aligned & A C=B D= a^2+a^2 =a 2 & O A=O B=O C=O D= a 2 2 = a 2 aligned Potential is a scalar quantity. Potential at the centre O due to given charge configuration is aligned & V= 1 4 ₀ [ (-Q) ( a 2 ) + (-q) ( a 2 ) + (2 q) ( a 2 ) + 2 Q ( a 2 ) ]=0 & -Q-q+2 q+2 Q=0 & or Q+q=0 or Q=-q aligned