Uniformly Charged Solid Sphere
For volume density rho, E_inside = rho r/(3 epsilon_0). For r >= R, E = kQ/r^2. These results require spherical symmetry and uniform density.
Why this shows up in the exam
Solid-sphere field graphs · Comparing fields of spheres · Finding force inside a uniform sphere
Learn the idea
Inside a uniform nonconducting sphere E grows linearly with r; outside it falls as 1/r². A Gaussian sphere encloses a fraction r³/R³ of the total charge, while its area grows as r², leaving an interior field proportional to r.
🧠 Memory hook: Uniform solid sphere: linear up, inverse-square down.
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/(3 epsilon₀) — interior field
- E(r>=R) = kQ/r² — exterior field
- Q_enclosed = (4/3) pi r³ rho — interior enclosed charge
How to approach it
- 1Check whether r is inside or outside
- 2Compute enclosed charge
- 3Apply Gauss and verify continuity at the surface
Common slip-ups that cost marks
- •Using the full charge for an interior point
- •Calling the sphere conducting
- •Missing continuity of E at r = R
🌟 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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