Question

A coil of mean area $400{\text{cm}}^2$ and having $1000\text{turns}$, is held perpendicular to a uniform magnetic field of $0.2\text{T}$. The coil is turned through ${90}^{\circ }$ in $\frac{1}{10}\text{seconds}$. Calculate the change in magnetic flux ?

• A. $10\text{Wb}$
• B. $-6\text{Wb}$
• C. $-8\text{Wb}$
• D. $12\text{Wb}$

Answer 1

The correct option is C $-8\text{Wb}$

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 ${90}^{\circ }$, the flux linked,
${\varphi }_2=NBA\cos \left({90}^{\circ }\right)=0$

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

$\Delta \varphi =-1000\times 0.2\times 400\times {10}^{-4}=-8\text{Wb}$

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