Physics - EMI/AC Question with Solution | TestHub

The magnetic flux through the coil is $\Phi =NBA=N(0.2t^2+0.5)A$. The area of the coil is $A=\pi r^2=\pi (0.05\text{ m}{)}^2=0.0025\pi {\text{ m}}^2$. The induced EMF is given by Faraday's law: $\text{EMF}=|-\frac{d\Phi }{dt}|=|-\frac{d}{dt}(N(0.2t^2+0.5)A)|=NA|\frac{d}{dt}(0.2t^2+0.5)|=NA(0.4t)$. At $t=2\text{ s}$, $\text{EMF}=(50)(0.0025\pi {\text{ m}}^2)(0.4\times 2\text{ T/s})=(50)(0.0025\pi )(0.8)\text{ V}=0.1\pi \text{ V}$. Using $\pi =3.14$, $\text{EMF}=0.1\times 3.14\text{ V}=0.314\text{ V}$. Converting to millivolts, $\text{EMF}=0.314\times 1000\text{ mV}=314\text{ mV}$.