Electric Charges & Fields
Class 12 · Electric Charges & Fields

Gaussian Surface — Sphere

E = 0 inside a uniformly charged shell, kQ/r² outside. Plot with live cursor.

Key Notes

01

Uniformly charged spherical shell: outside, E = kQ/r² (acts like point charge at center).

02

Inside the shell: E = 0 everywhere (a key Gauss's law result).

03

For solid uniform sphere of charge: E inside ∝ r, E outside same as point charge.

Formulas

Shell, outside

r > R.

Shell, inside

r < R.

Solid sphere, inside

Linear in r.

Important Points

These results are fundamental for satellites, planets (gravity), conductors.

At r=R there's a discontinuity for the shell: E jumps from 0 to kQ/R².

Gaussian Surface — Sphere notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.