Spherical and Cylindrical Capacitors
With vacuum or uniform linear dielectric and negligible end effects, concentric spherical or long coaxial conductors have capacitance determined by their radii and geometry.
Why this shows up in the exam
spherical capacitors · coaxial cables · isolated-sphere capacitance
Learn the idea
Curved capacitors require integrating the radial field between conductors. For concentric conductors, field lines spread with radius, so the flat-plate formula does not apply. Gauss law gives E(r), and its integral gives voltage.
🧠 Memory hook: Curved plates: Gauss first, integrate second.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- C_spherical = 4 pi epsilon ab/(b-a) — concentric spheres, inner radius a, outer radius b
- C_coaxial = 2 pi epsilon L/ln(b/a) — long coaxial cylinders, negligible end effects
- C_isolated sphere = 4 pi epsilon R — reference at infinity
How to approach it
- 1Use Gauss law for radial E
- 2Integrate from inner to outer conductor
- 3Form C=Q/Delta V and test limits
Common slip-ups that cost marks
- •Using epsilon A/d blindly for curved geometry
- •Swapping inner and outer radii in the logarithm
- •Ignoring end effects for a short cylinder
🌟 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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