If identical charges $( - q)$ are placed at each corner of a cube of side $b$, then electric potential energy of charge $( + q)$ which is placed at centre of the cube will be
AIPMT 2002, Medium
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(d) Length of the diagonal of a cube having each side $b$ is $\sqrt 3 \,b.$ So distance of centre of cube from each vertex is $\frac{{\sqrt 3 \,b}}{2}.$
Hence potential energy of the given system of charge is
$U = 8 \times \left\{ {\frac{1}{{4\pi {\varepsilon _0}}}.\frac{{( - q)\,(q)}}{{\sqrt 3 \,b/2}}} \right\} = \frac{{ - 4{q^2}}}{{\sqrt 3 \pi {\varepsilon _0}b}}$
Hence potential energy of the given system of charge is
$U = 8 \times \left\{ {\frac{1}{{4\pi {\varepsilon _0}}}.\frac{{( - q)\,(q)}}{{\sqrt 3 \,b/2}}} \right\} = \frac{{ - 4{q^2}}}{{\sqrt 3 \pi {\varepsilon _0}b}}$
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