Class 12 Physics: Electrostatics Derivations That Repeat

Coulomb's law to field

Start from the force between two point charges and divide by the test charge. The electric field is force per unit positive charge, and defining it that way makes superposition immediate.

Gauss's law and its three classics

Gauss's law states that total flux through a closed surface equals enclosed charge divided by the permittivity of free space. Three derivations follow directly: the infinite line charge, the infinite plane sheet and the uniformly charged spherical shell.

• Line charge — field falls as 1/r
• Plane sheet — field is independent of distance
• Spherical shell — zero inside, point-charge-like outside

Potential and capacitance

Potential is work per unit charge moved from infinity. From there, the parallel-plate capacitor derivation and the energy stored in a capacitor follow in four steps each — both are frequent five-mark questions.

Scoring the marks

Examiners award marks for the labelled diagram, the stated assumption, the symmetry argument and the final expression. Skipping the diagram costs a mark even when the algebra is perfect.