Solution
= Solution
<Faraday's law> states that the induced <electromotive force> equals minus the rate of change of linked <magnetic flux>:
$$
\boxed{\mathcal E=-\frac{d(N\Phi)}{dt}.}
$$
The minus sign expresses <Lenz's law>: the induced <electric current> acts to oppose the change in <magnetic flux>. For a fixed contour this is equivalent to $\oint\mathbf E\cdot d\boldsymbol\ell=-d\int\mathbf B\cdot d\mathbf S/dt$.