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The work required to assemble a system of two point charges q₁ and q₂ separated by distance r₁₂ from rest at infinity is
A(1/4πε₀) · q₁ · q₂ / r₁₂
B(1/4πε₀) · (q₁² + q₂²) / r₁₂
C(1/4πε₀) · q₁ · q₂ · r₁₂
D(1/4πε₀) · q₁ · q₂ / r₁₂²
Answer & Solution
Correct answer: A. (1/4πε₀) · q₁ · q₂ / r₁₂
Assembling the second charge against the first costs U = q₂ · V₁ = q₂ · (1/4πε₀)(q₁/r₁₂) = (1/4πε₀)(q₁q₂/r₁₂). The square-r-denominator form belongs to the force, not the energy.
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