Point-Charge Potential and Superposition
With zero potential chosen at infinity, the potential of stationary point charges is the algebraic sum of kq_i/r_i at a field point not occupied by a point charge.
Why this shows up in the exam
vertices and polygon centres · zero-potential loci · alternating infinite charge series
Learn the idea
Scalar potentials from point charges add algebraically. Each charge contributes an electrical height kq/r. Because potential is a scalar, add signed numbers rather than resolving directions.
🧠 Memory hook: Potential adds like signed numbers, not arrows.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- V = (1/(4 pi epsilon₀)) sum(q_i/r_i) — vacuum; reference V(infinity)=0
- U_test = q₀ V — test charge does not disturb the sources
How to approach it
- 1Draw distances from every source to the field point
- 2Attach each charge sign
- 3Add scalars and check symmetry
Common slip-ups that cost marks
- •Using vector components for potential
- •Using separation between source charges instead of distance to field point
- •Ignoring convergence or the chosen zero
🌟 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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