The EMF $\mathcal{E}$ in a closed circuit $C$ is defined as the closed line integral of the electric field ${\vec E}$ around the loop: $$\mathcal{E}=\oint_C{\vec E}\cdot d{\vec\ell}.$$
But in Section 7.1.3 of Introduction to Electrodynamics by David J. Griffiths (3rd edition), in the context of a closed rectangular loop of wire, which is moved in a static, uniform magnetic field, the emf $\mathcal{E}$ is defined as $$\mathcal{E}=\oint_C{\vec f}_{\rm mag}\cdot d{\vec\ell}$$ where ${\vec f}_{\rm mag}$ denotes the magnetic Lorentz force on the charge carriers in the wire. Between the two is the correct?
