 Solution

Faraday's law of induction states that the induced electromotive force around an oriented closed circuit equals the negative rate of change of linked magnetic flux. For a stationary circuit,Here $\mathbf{E}$ is electric field, $\mathbf{B}$ is magnetic flux density, and the oriented surface $A$ has the circuit as its boundary. For $N$ identical series turns, replace ${\Phi }_B$ by the total flux linkage $N{\Phi }_B$. Lenz's law supplies the sign: an induced electric current opposes the change of linked magnetic flux, in agreement with conservation of energy.

If the wire moves with local velocity $\mathbf{u}$, the more general electromotive force includes the magnetic Lorentz force per unit electric charge:The boundary and surface orientations in both expressions are related by the right-hand rule.