Question

A coil of mean area $500{\text{cm}}^2$ and having $1000$ turns is held perpendicular to a uniform field of $0.4\text{G}$. The coil is turned through ${180}^{\circ }$ in $\frac{1}{10}\text{s}$. Calculate the magnitude of average induced $\text{emf}$.

• A. $2\text{V}$
• B. $4\text{V}$
• C. $0.2\text{V}$
• D. $0.04\text{V}$

Answer 1

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

Initial flux linked with the coil is,

${\varphi }_1=NBA\cos \theta$

$=1000\times (0.4\times {10}^{-4}\times (500\times {10}^{-4})\cos 0^{\circ }$

$=2\times {10}^{-3}\text{Wb}$

Final flux linked with the coil,

${\varphi }_2=NBA\cos \theta$

$=1000\times (0.4\times {10}^{-4}\times (500\times {10}^{-4})\cos {180}^{\circ }$

$=-2\times {10}^{-3}\text{Wb}$

$\therefore$ Magnitude of average $\text{emf}$ induced in the loop be,

$E=\left|\frac{△\varphi }{△t}\right|=\frac{|{\varphi }_2-{\varphi }_1|}{△t}$

$=\frac{|-2\times {10}^{-3}-2\times {10}^{-3}|}{0.1}=0.04\text{V}$

Hence, option $\left(D\right)$ is the correct answer.