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(A) The electric potential $V$ at any corner of the square due to the charge $Q$ at the centre is given by $V = \frac{1}{4\pi \epsilon_0} \frac{Q}{r}$

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(A) The electric potential $V$ at any corner of the square due to the charge $Q$ at the centre is given by $V = \frac{1}{4\pi \epsilon_0} \frac{Q}{r}$,where $r$ is the distance from the centre to any corner.In a square of side $a$,the diagonal is $a\sqrt{2}$,so the distance from the centre to any corner is $r = \frac{a\sqrt{2}}{2} = \frac{a}{\sqrt{2}}$.Since the distance $r$ is the same for all four corners,the electric potential $V$ is the same at all corners.The work done $W$ in moving a charge $q$ between two points is given by $W = q(V_{final} - V_{initial})$.Since $V_{final} = V_{initial}$,the work done $W = q(V - V) = 0$.

$A$ square of side $a$ has a charge $Q$ at its centre. $A$ charge $q$ is placed at one of the corners. The work required to be done in moving the charge $q$ from this corner to the diagonally opposite corner is

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