Potential of Continuous Charge Distributions
For a specified charge density and reference V(infinity)=0 where valid, integrate the point-charge contribution over the actual distribution without vector resolution.
Why this shows up in the exam
potential of rings and arcs · axis potential of disks · finite line-charge integrals
Learn the idea
Break an extended charge into elements and integrate k dq/r. A ring, arc, disk, or line is a crowd of tiny point charges. Symmetry often makes every element equally distant or reduces the integral to one coordinate.
🧠 Memory hook: For potential, integrate distance-weighted charge, not field components.
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)) integral(dq/r) — finite distribution with V(infinity)=0
- dq = lambda dl = sigma dA = rho dTau — choose the density matching the source geometry
How to approach it
- 1Choose dl, dA, or dTau
- 2Express r from element to observation point
- 3Use symmetry, integrate, then set the reference
Common slip-ups that cost marks
- •Integrating the total charge again after using dq
- •Using an infinite-distribution absolute potential
- •Importing field cancellation into a scalar sum
🌟 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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