Faraday's Laws & Lenz's Law
Faraday's Law:
Induced emf in a circuit is proportional to the time rate of change of magnetic flux through it:
$$\mathcal{E} = -\frac{d\Phi_B}{dt}$$
Lenz's Law:
The polarity of induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux that produces it. (Consequence of the Law of Conservation of Energy).
Inductance
- Self Inductance ($L$): $\Phi = LI \implies \mathcal{E} = -L\frac{dI}{dt}$
- Solenoid of length $l$, area $A$, and $N$ turns: $L = \mu_0 \frac{N^2 A}{l}$.
- Mutual Inductance ($M$): $\Phi_2 = MI_1 \implies \mathcal{E}_2 = -M\frac{dI_1}{dt}$.
- Motional EMF: $\mathcal{E} = Bvl$ (for rod of length $l$ moving at velocity $v$ perpendicular to field $B$).
