Shell Theorem and Spherical Symmetry
Newton's shell theorem states that a spherically symmetric mass distribution produces the external field -GM r_hat/r^2, while a thin uniform spherical shell produces zero field and constant potential at every interior point.
Why this shows up in the exam
Fields of planets and shells · Concentric sphere-shell systems · Interior potential questions
Learn the idea
Outside a spherical body gravity acts as if all mass were central; a uniform shell gives zero field inside. Concentric spherical layers cancel their sideways pulls inside a shell, while an outside point sees the total mass concentrated at the centre.
🧠 Memory hook: A shell is field-free inside, not potential-free.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- g_out = GM/r² — magnitude outside a spherical source
- g_inside_shell = 0 — field anywhere inside a uniform thin shell
- V_inside_shell = -GM/R — constant interior potential when V(infinity)=0
How to approach it
- 1Identify shell, solid sphere, or layered body
- 2Split into spherical layers if needed
- 3Apply the correct inside or outside result
Common slip-ups that cost marks
- •Setting interior potential to zero
- •Using only enclosed mass without checking symmetry
- •Applying the point-mass rule inside a solid sphere
🌟 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.
A satellite moves in a circular orbit where GM = 4 x 10^14 m^3/s^2 and orbital radius is 2 x 10^6 m. Find its orbital speed.
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