# Talk:QB/d cp2.14

Mutual inductance: ${\displaystyle M{\tfrac {dI_{2}}{dt}}=N_{1}{\tfrac {d\Phi _{12}}{dt}}=-\varepsilon _{1}}$ where ${\displaystyle \Phi _{12}}$=flux through 1 due to current in 2. Reciprocity${\displaystyle M{\tfrac {dI_{1}}{dt}}=-\varepsilon _{2}}$
Self-inductance: ${\displaystyle N\Phi _{m}=LI\rightarrow \varepsilon =-L{\tfrac {dI}{dt}}}$
${\displaystyle L_{\text{solenoid}}\approx \mu _{0}N^{2}A\ell }$, ${\displaystyle L_{\text{toroid}}\approx {\tfrac {\mu _{0}N^{2}h}{2\pi }}\ln {\tfrac {R_{2}}{R_{1}}}}$, Stored energy=${\displaystyle {\tfrac {1}{2}}LI^{2}}$
${\displaystyle I(t)={\tfrac {\varepsilon }{R}}\left(1-e^{-t/\tau }\right)}$ in LR circuit where ${\displaystyle \tau =L/R}$.
${\displaystyle q(t)=q_{0}\cos(\omega t+\phi )}$ in LC circuit where ${\displaystyle \omega ={\sqrt {\tfrac {1}{LC}}}}$