EMI & AC — Induction & Inductance (Medium)

Quick Recap — Induction & Inductance

• Faraday / Lenz: $\varepsilon=-N\dfrac{d\Phi}{dt}$; the induced current opposes the change that produced it (energy conservation). Flux $\Phi=BA\cos\theta$.
• Motional emf: a rod of length $L$ moving at $v$ perpendicular to $B$ gives $\varepsilon=BLv$. A rod rotating about one end: $\varepsilon=\tfrac12 B\omega L^2$.
• Induced charge: $q=\dfrac{N\,\Delta\Phi}{R}$ (independent of how fast the flux changes).
• Self-inductance: $\varepsilon=-L\dfrac{dI}{dt}$; energy stored $=\tfrac12 LI^2$; solenoid $L=\mu_0 n^2 A l$. Mutual: $\varepsilon_2=-M\dfrac{dI_1}{dt}$.
• LR growth: $I=I_0\left(1-e^{-t/\tau}\right)$, time constant $\tau=\dfrac{L}{R}$.

Worked mini-example. A rod 0.4 m long slides at 10 m/s perpendicular to a 0.5 T field: $\varepsilon=BLv=0.5\times0.4\times10=2$ V.