Electricity & Magnetism

Electric fields, magnetic forces and electromagnetic induction

Electricity & Magnetism brings together the formulas that describe how charges, currents, and fields behave, from Coulomb’s Law and electric potential to magnetic forces and Faraday’s Law. It’s a useful reference for students, exam prep, and anyone working with circuits, sensors, motors, or other real-world systems, because these equations connect abstract physics to the technologies that power modern life.

Coulomb's Law

F = k\frac{q_1 q_2}{r^2}

Force between two point charges.

Electric Field

E = \frac{F}{q}

Force per unit charge at a point.

Field of a Point Charge

E = k\frac{q}{r^2}

Electric field around a point charge.

Electric Potential

V = k\frac{q}{r}

Potential due to a point charge.

Electric Potential Energy

U = k\frac{q_1 q_2}{r}

Energy of two interacting charges.

Gauss's Law

\Phi_E = \frac{Q_{enc}}{\varepsilon_0}

Electric flux through a closed surface.

Parallel-Plate Capacitance

C = \frac{\varepsilon_0 A}{d}

Capacitance from plate area and separation.

Magnetic Force on a Charge

F = qvB\sin\theta

Force on a moving charge in a magnetic field.

Force on a Current Wire

F = BIL\sin\theta

Force on a current-carrying conductor.

Field of a Straight Wire

B = \frac{\mu_0 I}{2\pi r}

Magnetic field around a long straight wire.

Field Inside a Solenoid

B = \mu_0 n I

Magnetic field inside an ideal solenoid.

Faraday's Law

\mathcal{E} = -N\frac{d\Phi_B}{dt}

Induced EMF from changing magnetic flux.

Magnetic Flux

\Phi_B = BA\cos\theta

Flux through a surface in a magnetic field.

Motional EMF

\mathcal{E} = BLv

EMF from a conductor moving through a field.

Cyclotron Frequency

f = \frac{qB}{2\pi m}

Rotation frequency of a charge in a magnetic field.

EM Energy Density

u = \tfrac{1}{2}\varepsilon_0 E^2 + \frac{B^2}{2\mu_0}

Energy stored per unit volume in EM fields.

Speed of Light (EM)

c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}

Light speed from vacuum constants.

Maxwell's Equations

\begin{aligned}\nabla\cdot\mathbf{E}&=\tfrac{\rho}{\varepsilon_0} & \nabla\times\mathbf{E}&=-\tfrac{\partial\mathbf{B}}{\partial t}\\ \nabla\cdot\mathbf{B}&=0 & \nabla\times\mathbf{B}&=\mu_0\mathbf{J}+\mu_0\varepsilon_0\tfrac{\partial\mathbf{E}}{\partial t}\end{aligned}

The four equations that describe how electric and magnetic fields are generated by charges and currents, and how they interact — the complete classical theory of electromagnetism.