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Four equal point charges q are placed at the vertices of a regular tetrahedron of edge length R. The total electrostatic potential energy of this arrangement is alpha*k*q²/R. Find alpha.

1. 6
2. 3
3. 2
4. 1

Correct answer: 6

Solution

Total electrostatic energy is the sum of pair interaction energies. With 4 charges there are C(4,2) = 6 pairs, and in a regular tetrahedron all pair separations equal the edge R. Each pair contributes k*q²/R, so U = 6*k*q²/R, giving alpha = 6.

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