Potential Energy of Charge Configurations
For stationary point charges assembled quasistatically from infinity, total electrostatic potential energy is the sum k q_i q_j/r_ij over i<j.
Why this shows up in the exam
charges on polygons · moving one charge in a fixed configuration · comparing assembled arrangements
Learn the idea
Configuration energy counts each interacting pair once. Building a set of charges requires work against interactions already present. Add the energy of every unordered pair, not the potential of a charge with itself.
🧠 Memory hook: Pairs once: i less than j.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U = (1/(4 pi epsilon₀)) sum_(i<j)(q_i q_j/r_ij) — distinct stationary point-charge pairs
- U_test = q V_external — V excludes the test charge self-potential
How to approach it
- 1List every unordered pair
- 2Write each signed product over separation
- 3Use symmetry to group equal terms
Common slip-ups that cost marks
- •Double-counting pairs
- •Including self-energy of ideal point charges
- •Losing signs of unlike-charge pairs
🌟 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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