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.