Electrostatic Equilibrium and Stability
For one coordinate, equilibrium occurs where dU/dx=0; it is stable when d^2U/dx^2>0 and unstable when d^2U/dx^2<0, subject to the allowed constraints.
Why this shows up in the exam
zero-force points between charges · turning points and small disturbances · dipole alignment stability
Learn the idea
Equilibrium needs zero force; stability needs potential energy to rise for small displacements. A ball can balance on a hilltop or rest in a bowl. Both have zero slope, but only the bowl restores it after a small push.
🧠 Memory hook: Zero slope finds balance; curvature decides stability.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F_x = -dU/dx = -q dV/dx — one-dimensional conservative motion
- d²U/dx² > 0 — local stable equilibrium
How to approach it
- 1Find where force or energy slope vanishes
- 2Apply the physical domain constraints
- 3Test curvature or a small displacement
Common slip-ups that cost marks
- •Calling every zero-field point stable
- •Testing V curvature without multiplying by charge sign
- •Ignoring constrained directions
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
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