The potential energy of a particle is U(r)=A/r²-B/r, where A, B>0. Find distance for stable equilibrium.
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Question

The potential energy of a particle is U(r)=A/r²−B/r, where A,B>0. Find distance for stable equilibrium.

G1 Physics · Accepted Answer

Step 1 — Principle: Equilibrium occurs where dU/dx = 0; stable equilibrium also requires a local minimum of U. Step 2 — Working: At equilibrium dU/dr=−2A/r³+B/r²=0, so r=2A/B. Step 3 — Working: The second derivative at that point is positive, verifying stable equilibrium. Correct answer: B — 2A/B.