Select the expression that gives the instantaneous magnitude of the induced electromotive force for a coil of $N$ turns in calculus form.

How is the instantaneous induced emf related to the average induced emf over a time interval?

A fixed $50$-turn coil with constant area $A$ is placed in a constant magnetic field $B$, and only the angle $\theta$ changes with time. Identify the quantities that may be taken outside the derivative when differentiating the flux.

A $12$-turn conducting frame sits in a constant magnetic field of $0.60$ T with $\theta =0^{\circ }$. Its area increases at a rate of $0.015{\text{ m}}^2/\text{s}$. Calculate the magnitude of the induced electromotive force.

A $25$-turn rectangular coil with dimensions $0.30$ m by $0.20$ m is oriented such that the angle between the magnetic field and the area normal is $\theta ={30}^{\circ }$. The magnetic field varies with time according to $B\left(t\right)=(1.0+0.50t^2)$ T. Calculate the magnitude of the induced electromotive force at $t=4.0$ s.