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Each corner of a cube of side l has a negative charge, -q. The electrostatic potential energy of a charge q at the centre of the cube is

1. -4q² / √2πϵ₀l
2. -√3q² / 4πϵ₀l
3. 4q² / √2πϵ₀l
4. 4q² / √3πϵ₀l

Correct answer: -√3q² / 4πϵ₀l

Solution

The potential energy at the center due to one charge is given by k(-q)(q)/r, where r is the distance from the center to a corner, which is l√3/2. Summing contributions from all 8 charges, the total potential energy is -√3q² / 4πϵ₀l.

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