= Solution
<Faraday's law of induction> states that the induced <electromotive force> around a material <electrical circuit> equals the negative rate of change of its linked <magnetic flux>:
$$
\boxed{\mathcal E=\oint_{C(t)}(\mathbf E+\mathbf v\times\mathbf B)\cdot d\boldsymbol\ell=-\frac{d}{dt}\int_{S(t)}\mathbf B\cdot d\mathbf S.}
$$
The <surface> orientation and direction around its boundary are related by the <right-hand rule>. <Lenz's law> supplies the physical meaning of the minus sign: the induced <electric current> produces a <magnetic field> opposing the change in linked <magnetic flux>. For a stationary contour the local form is $\nabla\times\mathbf E=-\partial_t\mathbf B$; for this moving wire, the magnetic <Lorentz force> term is also needed in the <electromotive force>.
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