Question

A coil of area $500c{m}^2$ having 1000 turns is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude $4{10}^{-5}weber/m^2$. If it is rotated by $180$ degree about an axis passing through one of its diameter in $0.1$ sec, find the average induced emf.

• A. $zero.$
• B. $30mV$
• C. $40mV$
• D. $50mV$

Answer 1

Answer: (C)

$40mV$

Area of the coil $A=500c{m}^2=0.05m^2$
Number of coil $N=1000$
Magnetic field $B=4\times {10}^{-5}Wb/m^2$
Magnetic flux passing through the coil initially $(\theta =0^o)$,
${\varphi }_i=NBA\cos \varphi =1000\times 4\times {10}^{-5}\times 0.05\times \cos 0^o=0.002Wb$
Magnetic flux passing through the coil finally $(\theta ={180}^o)$,
${\varphi }_f=NBA\cos \varphi =1000\times 4\times {10}^{-5}\times 0.05\times \cos {180}^o=-0.002Wb$
Thus change of flux $\Delta \varphi ={\varphi }_i-{\varphi }_f=0.002-(-0.002)=0.004Wb$
Change in time $\Delta t=0.1s$
Thus average emf induced $E=\frac{\Delta \varphi }{\Delta t}=\frac{0.004}{0.1}=40mV$