Question

A coil of mean area $500{\text{cm}}^2$ and having $1000\text{turns}$, is held perpendicular to a uniform magnetic field of $0.4\times {10}^{-4}\text{T}$. The coil is turned through ${180}^{\circ }$ in $\frac{1}{10}\text{seconds}$. Calculate the average induced emf?

• A. $4\text{V}$
• B. $0.4\text{V}$
• C. $0.04\text{V}$
• D. $0.8\text{V}$

Answer 1

The correct option is C $0.04\text{V}$

When the plane of coil is perpendicular to the magnetic field, the angle between area $\overrightarrow{A}$ and field $\overrightarrow{B}$ is $0^{\circ }$.

The flux linked with coil,
${\varphi }_1=NBA\cos 0^{\circ }=NBA$

When the coil is turned through ${180}^{\circ }$, the flux linked,
${\varphi }_2=NBA\cos \left({180}^{\circ }\right)=-NBA$

$\therefore$ Change in flux $\Delta \varphi ={\varphi }_2-{\varphi }_1=-2NBA$

The magnitude of induced emf is,

$E=\left|\frac{\Delta \varphi }{\Delta t}\right|=\frac{2NBA}{\Delta t}$

$E=\frac{2\times 1000\times 0.4\times {10}^{-4}\times 500\times {10}^{-4}}{0.1}$

$E=0.04\text{V}$

Hence, option ($C$) is the correct answer.