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 :

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 = - (1/q) (C)  Q = q  (D) Q = (1/q)

Tardigrade Admin · Accepted Answer

Let the side length of square be 'a' then potential at centre O is V=(k(-Q)/((a)√2))+(k(-q)/(a)√2)+(k(2 q)/(a)√2)+(k(2 Q)/(a)√2)=0 =Q-q+2 q+2 Q=0 ⇒ Q ⇒ +q=0 (Given) Q=-q

Q. 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 :

$Q = - q$

$Q = - \frac{1}{q}$

$Q = q$

$Q = \frac{1}{q}$

Let the side length of square be 'a' then potential at centre $O$ is
$V = \frac{k ( - Q )}{( \frac{a}{2} )} + \frac{k ( - q )}{\frac{a}{2}} + \frac{k ( 2 q )}{\frac{a}{2}} + \frac{k ( 2 Q )}{\frac{a}{2}} = 0$
$= Q - q + 2 q + 2 Q = 0$
$\Rightarrow Q$
$\Rightarrow + q = 0$ (Given)
$Q = - q$

Q. 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 :

Q=−q

Q=−q1​

Q=q

Q=q1​