A coil having an area $A_{0}$ is placed in a magnetic field. The field intensity changes from $B_{0}$ to $4 B_{0}$ in time interval of ‘t’. The magnitude of emf induced in the coil will be _____.

\frac{A_{0} B_{0}}{t}

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\frac{3 A_{0} B_{0}}{t}

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\frac{3 B_{0}}{A_{0} t}

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\frac{4 B_{0}}{A_{0} t}

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Solution

The correct option is B $\frac{3 A_{0} B_{0}}{t}$
The emf induced in a coil of turns $N$ , area of cross section $A$ is given by

$e m f = - \frac{Δ (B A)}{t}$ $= - A_{0} (4 B_{0} - B_{0})$

where $B_{2} - B_{1}$ is the change in the magnetic field.
$⟹ e = \frac{- 3 A_{0} B_{0}}{t}$

Hence, the magnitude $| e | = \frac{3 A_{0} B_{0}}{t}$

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A coil having an area A0 is placed in a magnetic field. The field intensity changes from B0 to 4B0 in time interval of ‘t’. The magnitude of emf induced in the coil will be _____.

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A coil having an area $A_{0}$ is placed in a magnetic field. The field intensity changes from $B_{0}$ to $4 B_{0}$ in time interval of ‘t’. The magnitude of emf induced in the coil will be _____.