= Solution
<Faraday's law> relates induced <electromotive force> to the rate of change of <magnetic flux linkage>. For a coil with $N$ turns and a consistent right-hand orientation,
$$
\boxed{\mathcal E=-\frac{d(N\Phi_B)}{dt}.}
$$
<Flux> can change through field variation or circuit motion. <Lenz's law> is the minus sign: the induced current's field opposes the <flux> change, consistent with <energy> conservation. It opposes the change rather than necessarily opposing the original field.
For a linear fixed-geometry <inductor>, $N\Phi_B=LI$ and the self-induced <electromotive force> is $-L\,dI/dt$. The passive terminal <voltage> drop is instead $V=L\,dI/dt$. The stored magnetic <energy> is
$$
\boxed{U_B=\int_0^I LI'\,dI'=\tfrac12LI^2.}
$$
<Inductance> is measured in henries. Transformers use <mutual inductance>: changing one winding's current induces an <electromotive force> in another.
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