Equipotential Surfaces
An equipotential surface has constant V. Therefore dV=0 for tangential displacement and E=-grad V has no tangential component in electrostatics.
Why this shows up in the exam
identifying equipotential geometry · zero-work paths · relations between field lines and surfaces
Learn the idea
No work is done along an equipotential, and electric field crosses it normally. A contour map joins equal heights; walking along one contour changes no potential. The steepest descent is perpendicular to the contour and points with the electric field.
🧠 Memory hook: Same V means zero work, not necessarily zero field.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W_field along equipotential = -q Delta V = 0 — same initial and final potential
- E = -grad V — electrostatic field is normal toward decreasing V
How to approach it
- 1Test whether V is constant
- 2Use symmetry to sketch the surface
- 3Draw E normal toward lower V
Common slip-ups that cost marks
- •Claiming E=0 on every equipotential
- •Drawing field tangent to an equipotential
- •Ignoring charge sign when discussing force
🌟 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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