Electrostatics - Formula Sheet

Core Formulas

Coulomb's Law (Force): \(F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}\)
Where \(F\) is force, \(q\) represents charge magnitudes, \(r\) is separation distance, and \(\epsilon_0\) is vacuum permittivity.

Electric Field of a Point Charge: \(E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}\)
Where \(E\) is the electric field strength at distance \(r\) from charge \(q\).

Quantization of Electric Charge: \(q = ne\)
Where \(n\) is an integer and \(e\) is the fundamental unit of charge (\(1.6 \times 10^{-19}\) C).

Electric Dipole Moment: \(p = 2aq\)
Where \(2a\) is the distance between the two charges of magnitude \(q\).

Torque on a Dipole: \(\tau = pE \sin \theta\)
Where \(\tau\) is torque, \(p\) is dipole moment, \(E\) is external field, and \(\theta\) is the alignment angle.

Electrostatic Potential: \(V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}\)
Where \(V\) is the potential at distance \(r\) from a source charge \(q\).

Potential Energy of System: \(U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r}\)
Where \(U\) is the stored work done to assemble the charges.

Gauss's Law: \(\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{encl}}{\epsilon_0}\)
Where \(\Phi_E\) is total flux and \(Q_{encl}\) is the net charge enclosed by a surface.

Capacitance: \(C = \frac{Q}{V}\)
Where \(C\) is capacitance, \(Q\) is charge, and \(V\) is potential difference.

Parallel Plate Capacitor: \(C = \frac{\epsilon_0 A}{d}\)
Where \(A\) is the area of the plates and \(d\) is their separation distance.

Energy Stored in Capacitor: \(U = \frac{1}{2}CV^2\)
Where \(U\) is the stored electrical energy.