Field of a Uniform Spherical Shell
For a thin uniform spherical shell, E = 0 for r < R and E = kQ/r^2 for r > R. The ideal surface field is discontinuous by sigma/epsilon_0.
Why this shows up in the exam
Shell field graphs · Field at a shell surface · Shell-theorem force problems
Learn the idea
A uniformly charged spherical shell has zero interior field and acts like a point charge outside. Symmetry makes the field equally strong over a concentric Gaussian sphere. Inside, no charge is enclosed; outside, the full shell charge is enclosed.
🧠 Memory hook: Empty inside, point-charge 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) = 0 — interior field of a uniform spherical shell
- E(r>R) = kQ/r² — exterior field
- E_out - E_in = sigma/epsilon₀ — normal-field jump across the charged surface
How to approach it
- 1Locate the point relative to R
- 2Choose a concentric Gaussian sphere
- 3Use enclosed charge and state the surface limit
Common slip-ups that cost marks
- •Extending kQ/r² into the hollow interior
- •Averaging surface limits when one-sided field is asked
- •Applying shell symmetry to a nonuniform shell
🌟 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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