Electrostatic Equilibrium and Stability
At equilibrium F(x_0) = 0. For a small displacement xi, stable one-dimensional equilibrium has F approximately -k_eff xi with k_eff > 0.
Why this shows up in the exam
Small-displacement charge systems · Testing stable and unstable null points · Electrostatic SHM approximations
Learn the idea
Zero force gives equilibrium; the force after a small displacement decides whether it is stable. A charge can sit at a balance point yet move away after the slightest nudge. Stability requires the nearby force to point back toward equilibrium.
🧠 Memory hook: Zero force locates equilibrium; the slope tells its fate.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F(x₀) = 0 — equilibrium condition
- F approximately -k_eff xi — restoring-force test for small displacement
How to approach it
- 1Find the balance point
- 2Displace in the stated direction
- 3Check whether the leading force is restoring
Common slip-ups that cost marks
- •Calling every zero-force point stable
- •Keeping only zeroth-order terms
- •Ignoring a transverse displacement
🌟 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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