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(D) The work done $W$ in moving a charge $q_0$ from point $I$ to $F$ is given by $W = q_0 (V_F - V_I)$.Here,the charge being moved is $q_0 = -q$.The p

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$\frac{4 q^2}{\sqrt{3} \pi \epsilon_0 a}$

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(D) The work done $W$ in moving a charge $q_0$ from point $I$ to $F$ is given by $W = q_0 (V_F - V_I)$.Here,the charge being moved is $q_0 = -q$.The potential at infinity is $V_F = 0$.The distance of each corner from the centre of the cube of side $a$ is $r = \frac{\sqrt{3}}{2} a$.The potential at the centre $V_I$ due to $8$ charges $q$ is $V_I = 8 	imes \frac{1}{4 \pi \epsilon_0} \frac{q}{r} = 8 	imes \frac{1}{4 \pi \epsilon_0} \frac{q}{(\sqrt{3} a / 2)} = \frac{4 q}{\sqrt{3} \pi \epsilon_0 a}$.Therefore,$W = -q (0 - V_I) = q V_I = q \left( \frac{4 q}{\sqrt{3} \pi \epsilon_0 a} ight) = \frac{4 q^2}{\sqrt{3} \pi \epsilon_0 a}$.

Eight equal charges $q$ are placed at each corner of a cube of side $a$. The work done in carrying a charge $-q$ from its centre to infinity is:

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