Question 14 of 153

The magnetic field B crossing normally a square metallic plate of area $4{m}^{2}$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $t=2s$ to $t=4s$, is _____ $mV$.

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Answer: 8

From the graph, it can be seen that the value of the magnetic field at $t=2s$ is $4mT$, whereas the magnetic field at $t=4s$ is $8mT$.
The formula to calculate the magnitude of the induced emf is given by
$\begin{matrix}{\epsilon }_{\text{ind}} & = & \dfrac{d\phi }{dt} \\ & = & \dfrac{d}{dt}\left(BA\right) \\ & = & A\dfrac{dB}{dt}...\left(1\right)\end{matrix}$
$\dfrac{dB}{dt}$ is the slope of the given graph.
Hence, the value of the induced emf can be calculated as follows:
$\begin{matrix}{\epsilon }_{\text{ind}} & = & 4{m}^{2}\times \left(\dfrac{8mT-4mT}{4s-2s}\right) \\ & = & 8mV\end{matrix}$