Question 288: Electromagnetic Induction

Question

A coil having effective area '$$A$$' is held with its plane normal to a magnitude field of induction '$$\mathrm{B}$$'. The magnetic induction is quickly reduced to $$25 \%$$ of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be

Accepted Answer

The formula for induced emf is $$\mathrm{e}=\frac{\Delta \phi}{\Delta \mathrm{t}}$$, where $$\phi=\mathrm{BA}$$
Here, the area is constant and the magnetic field is changing.
$$\begin{aligned}
& 	herefore & \Delta \phi & =\Delta \mathrm{BA} \
& 	herefore & \Delta \phi & =\mathrm{A} \cdot \Delta \mathrm{B} \
& 	herefore & \Delta \mathrm{B} & =\mathrm{B}_1-\mathrm{B}_2
\end{aligned}$$
$$\mathrm{B}_1=\mathrm{B} 	ext { and } \mathrm{B}_2=\frac{25}{200} \mathrm{~B}=\frac{1}{4} \mathrm{~B}$$
$$\begin{aligned}
& 	herefore \quad \mathrm{B}=\mathrm{B}-\frac{1}{4} \mathrm{~B} \
& 	herefore \quad \mathrm{B}=\frac{3}{4} \mathrm{~B}
\end{aligned}$$
Substituting the values,
$$\begin{aligned}
\mathrm{e} & =\frac{\Delta \phi}{\Delta \mathrm{t}} \
\mathrm{e} & =\frac{\mathrm{A} 	imes \frac{3}{4} \mathrm{~B}}{1} \
	herefore \quad \mathrm{e} & =\frac{3}{4} \mathrm{AB}
\end{aligned}$$

Answer

$$\frac{\mathrm{BA}}{4}$$

Answer

$$\frac{\mathrm{BA}}{2}$$

Answer

$$\frac{3 \mathrm{BA}}{8}$$

Answer

$$\frac{3 \mathrm{BA}}{4}$$

Electromagnetic Induction

A coil having effective area '$A' is held with its plane normal to a magnitude field of induction '\mathrm{B}'. The magnetic induction is quickly reduced to 25 \%$ of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be

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