Potential of Spherical Shells and Spheres
For spherical symmetry and V(infinity)=0, use Gauss-law field outside and integrate inward; a conductor is equipotential, while a uniform volume charge has a nonzero interior field.
Why this shows up in the exam
centre and surface potentials · piecewise spherical graphs · nested spherical shells
Learn the idea
A shell is constant inside; a uniformly charged solid sphere varies quadratically inside. Inside a charged conducting shell there is no field, so the potential stays at its surface value. Inside a nonconducting solid sphere, enclosed charge grows with radius and the potential changes smoothly.
🧠 Memory hook: No field inside a shell means flat potential, not zero potential.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- V_shell(r<=R) = kQ/R; V(r>=R)=kQ/r — thin spherical shell or conducting sphere
- V_solid(r<=R)=kQ(3R²-r²)/(2R³) — uniformly charged nonconducting solid sphere
How to approach it
- 1Identify shell, conductor, or volume charge
- 2Write the piecewise region
- 3Check continuity at r=R
Common slip-ups that cost marks
- •Setting interior potential to zero
- •Using kQ/r inside a shell
- •Confusing conducting and uniformly charged solid spheres
🌟 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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