A force field in the xy-plane has components Fₓ = 2xy + y² and Fᵧ = x² + 2xy. Which statements are correct?
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Question

A force field in the xy-plane has components Fₓ = 2xy + y² and Fᵧ = x² + 2xy. Which statements are correct?

G1 Physics · Accepted Answer

∂Fₓ/∂y = 2x + 2y and ∂Fᵧ/∂x = 2x + 2y, so the field is conservative. Hence work is path independent and closed-loop work is zero. Since F = −∇U, one valid potential is U = −(x²y + xy²) + C.