Cylindrical Charge Distributions
For an infinite solid cylinder of density rho and radius R, E_inside = rho r/(2 epsilon_0) and E_outside = rho R^2/(2 epsilon_0 r).
Why this shows up in the exam
Uniform charged cylinders · Cylindrical shells · Circular motion around a charged cylinder
Learn the idea
Cylindrical symmetry turns volume or surface charge into radial fields found with a coaxial Gaussian cylinder. Inside a uniformly charged solid cylinder, enclosed charge grows as r² and Gaussian area as r, so E grows linearly. Outside, the field falls as 1/r.
🧠 Memory hook: Cylinder: linear inside, one-over-r outside.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E(r<R) = rho r/(2 epsilon₀) — inside a uniform infinite solid cylinder
- E(r>R) = rho R²/(2 epsilon₀ r) — outside the cylinder
How to approach it
- 1Choose a coaxial Gaussian cylinder
- 2Compute enclosed charge per length
- 3Separate inside and outside cases
Common slip-ups that cost marks
- •Using spherical factors of three
- •Including end-cap flux for an infinite cylinder
- •Applying the result when axial symmetry is broken
🌟 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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