Magnetic flux: Φ = BA cos θ; unit: Weber (Wb); maximum when B is perpendicular to the surface (θ = 0°); dimensional formula [M $L^{2}$ $T^{-2}$ $A^{-1}$].

Faraday's first law: A changing magnetic flux through a circuit induces an EMF.

Faraday's second law: EMF = −dΦ/dt (for a single turn); EMF = −N(dΦ/dt) for N turns. The negative sign represents Lenz's law.

Lenz's law: The induced current always opposes the change in flux that caused it. This is a consequence of conservation of energy. If the induced current aided the flux change, energy would be created without input.

Motional EMF: ε = Bvl when the rod (length l), velocity v, and field B are mutually perpendicular. Polarity determined by F = qv × B (right-hand rule). The higher potential end is where positive charges accumulate.

Rotating coil: EMF = NBAω sin(ωt); peak EMF ε_{0} = NBAω when coil plane is parallel to B (flux = 0, rate of change maximum).

Self-inductance: ε = −L(dI/dt); L = μ_{0}$n^{2}$Al for solenoid; unit: henry (H); dimensional formula [M $L^{2}$ $T^{-2}$ $A^{-2}$].

Energy in inductor: U = ½$LI^{2}$ (stored in magnetic field); this is analogous to U = ½$CV^{2}$ in a capacitor.

Mutual inductance: ε_{2} = −M(d$I_{1}$/dt); M = μ_{0}n_{1}n_{2}Al for coaxial solenoids. M is symmetric: $M_{12}$ = $M_{21}$.

Eddy currents: Induced in bulk conductors by changing flux. Useful in induction furnaces, electromagnetic braking, speedometers. Minimized by lamination (thin insulated sheets break current paths).

Back EMF: In an inductor, ε = −L(dI/dt) opposes changes in current — the electrical analogue of inertia. Zero for steady DC (dI/dt = 0).

Induced charge: q = N$\Delta$Φ/R — depends only on total flux change, not the rate. Measured by ballistic galvanometer.

Key dimensional formulas: [Φ] = [M $L^{2}$ $T^{-2}$ $A^{-1}$]; [EMF] = [M $L^{2}$ $T^{-3}$ $A^{-1}$]; [L] = [M $L^{2}$ $T^{-2}$ $A^{-2}$].