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 $t = 2 s$ to $t = 4 s$ , is _____ $m V$ .

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TestHub · Accepted Answer

From the graph, it can be seen that the value of the magnetic field at $t = 2 s$ is $4 mT$ , whereas the magnetic field at $t = 4 s$ is $8 mT$ .

The formula to calculate the magnitude of the induced emf is given by

$\begin{array}{rcl} ε_{ind} & = & \frac{d ϕ}{d t} \\ = & \frac{d}{d t} (B A) \\ = & A \frac{d B}{d t} . . . (1) \end{array}$

$\frac{d B}{d t}$ is the slope of the given graph.

Hence, the value of the induced emf can be calculated as follows:

$\begin{array}{rcl} ε_{ind} & = & 4 m^{2} \times (\frac{8 mT - 4 mT}{4 s - 2 s}) \\ = & 8 mV \end{array}$

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