Question
Four point charges $$ - Q, - q,2q$$ and $$2Q$$ 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
A.
$$Q = - q$$
B.
$$Q = - \frac{1}{q}$$
C.
$$Q = q$$
D.
$$Q = \frac{1}{q}$$
Answer :
$$Q = - q$$
Solution :
As, shown in figure
If potential at centre is zero, then $${V_1} + {V_2} + {V_3} + {V_4} = 0$$
$$\eqalign{ & \Rightarrow - \frac{{kQ}}{r} - \frac{{kq}}{r} + \frac{{k2Q}}{r} + \frac{{k2q}}{r} = 0 \cr & \Rightarrow - Q - q + 2q + 2Q = 0 \cr & \therefore Q = - q \cr} $$
As, shown in figure
If potential at centre is zero, then $${V_1} + {V_2} + {V_3} + {V_4} = 0$$
$$\eqalign{ & \Rightarrow - \frac{{kQ}}{r} - \frac{{kq}}{r} + \frac{{k2Q}}{r} + \frac{{k2q}}{r} = 0 \cr & \Rightarrow - Q - q + 2q + 2Q = 0 \cr & \therefore Q = - q \cr} $$