Solution
= Solution
<Faraday's law> states
$$
\boxed{\mathcal E=\oint\mathbf E\cdot d\boldsymbol\ell=-\frac{d\Phi_B}{dt}}
$$
for a stationary loop, with $\Phi_B=\int\mathbf B\cdot d\mathbf S$ and consistent contour and area orientations. The minus sign expresses <Lenz's law>: the induced response opposes the change of <magnetic flux>. An emf can exist across an open loop even when no conduction current flows.