Identical charges (-q) are placed at each cor | vedclass

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(D) The length of the body diagonal of a cube with side $b$ is $\sqrt{3}b$.Therefore,the distance from the center of the cube to each corner is $r = \

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$\frac{-4q^2}{\sqrt{3}\pi\varepsilon_0 b}$

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(D) The length of the body diagonal of a cube with side $b$ is $\sqrt{3}b$.Therefore,the distance from the center of the cube to each corner is $r = \frac{\sqrt{3}b}{2}$.The electrostatic potential energy $U$ of a charge $q_2$ at a distance $r$ from a charge $q_1$ is given by $U = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r}$.Since there are $8$ such charges of $(-q)$ at the corners and a charge $(+q)$ at the center,the total potential energy is:$U = 8 	imes \left[ \frac{1}{4\pi\varepsilon_0} \cdot \frac{(-q)(q)}{\frac{\sqrt{3}b}{2}} ight]$$U = 8 	imes \left[ \frac{1}{4\pi\varepsilon_0} \cdot \frac{-2q^2}{\sqrt{3}b} ight]$$U = \frac{-16q^2}{4\sqrt{3}\pi\varepsilon_0 b} = \frac{-4q^2}{\sqrt{3}\pi\varepsilon_0 b}$.

Identical charges $(-q)$ are placed at each corner of a cube of side $b$. The electrostatic potential energy of a charge $(+q)$ placed at the center of the cube is:

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