If identical charges ( - q) are placed at each corner of a cube of side b , then electric potential

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2. Electric Potential and Capacitance

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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

$\frac{{8\sqrt 2 {q^2}}}{{4\pi {\varepsilon _0}b}}$

$\frac{{ - 8\sqrt 2 {q^2}}}{{\pi {\varepsilon _0}b}}$

$\frac{{ - 4\sqrt 2 {q^2}}}{{\pi {\varepsilon _0}b}}$

$\frac{{ - 4{q^2}}}{{\sqrt 3 \pi {\varepsilon _0}b}}$

(AIPMT-2002)

Solution

(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
$U = 8 \times \left\{ {\frac{1}{{4\pi {\varepsilon _0}}}.\frac{{( – q)\,(q)}}{{\sqrt 3 \,b/2}}} \right\} = \frac{{ – 4{q^2}}}{{\sqrt 3 \pi {\varepsilon _0}b}}$

Standard 12

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Solution

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