OpenStax University Physics/E&M/Inductance

For quiz at QB/d_cp2.14
Unit of inductance = Henry (H)=1V·s/A

Mutual inductance: $$ M\tfrac{dI_2}{dt}=N_1\tfrac{d\Phi_{12}}{dt}=-\varepsilon_1$$ where $$ \Phi_{12}$$=flux through 1 due to current in 2. Reciprocity: $$M\tfrac{dI_1}{dt}=-\varepsilon_2$$

Self-inductance: $$N\Phi_m=LI\rightarrow\varepsilon=-L\tfrac{dI}{dt}$$

$$L_\text{solenoid}\approx\mu_0N^2A\ell$$, $$L_\text{toroid}\approx\tfrac{\mu_0N^2h}{2\pi}\ln\tfrac{R_2}{R_1}$$, Stored energy=$$\tfrac 12 LI^2$$

$$I(t)=\tfrac\varepsilon R \left(1-e^{-t/\tau}\right)$$ in LR circuit where $$\tau=L/R$$.

$$q(t)=q_0\cos(\omega t+\phi)$$ in LC circuit where $$\omega=\sqrt{\tfrac{1}{LC}}$$