Summary

• Magnetic Flux: $\Phi_B = \vec{B} \cdot \vec{A} = BA\cos\theta$; SI unit: weber (Wb).
• Faraday’s Law: Induced emf $\mathcal{E} = -\frac{d\Phi_B}{dt}$; magnitude $|\mathcal{E}| = N\frac{d\Phi_B}{dt}$ for $N$ turns.
• Lenz’s Law: Induced current opposes the change in flux; gives the negative sign in Faraday’s law.
• Motional emf: $\mathcal{E} = Blv$ for a rod of length $l$ moving at speed $v$ perpendicular to uniform $B$.
• Eddy Currents: Looping currents induced in bulk conductors; cause heating and damping (used in brakes, induction furnaces).
• Self-Inductance: $L = \frac{N\Phi_B}{I}$; emf $\mathcal{E} = -L\frac{dI}{dt}$; solenoid: $L = \mu_0 n^2 A l$.
• Mutual Inductance: $M = \frac{N_2\Phi_{21}}{I_1}$; emf in coil 2: $\mathcal{E}_2 = -M\frac{dI_1}{dt}$.
• Energy in Inductor: $U = \frac{1}{2}LI^2$; energy density $u = \frac{B^2}{2\mu_0}$.
• AC Generator: Rotating coil in $B$ produces sinusoidal emf $\mathcal{E} = NBA\omega\sin\omega t$.

Physical quantities, symbols, dimensions and units used in this chapter.