Question

A rectangular coil has $60$ turns and its length and width is $20cm$. and $10cm$ respectively. The coil rotates at a speed of $1800$ rotation per minute in a uniform magnetic field of $0.5T$ about its one of the diameter. Calculate maximum induced emf will be

Answer 1

Given that,

Number of turns $N=60$

Length $l=20cm$

Width $b=10cm$

Magnetic field $B=0.5T$

Rotation per min $f=1800$

We know that,

$\varphi =\left(AB\cos \theta \right)N$

$\varphi =NAB\cos \omega t$

$\frac{-d\varphi }{dt}=\epsilon$

$\epsilon =-\frac{d\left(NAB\cos \omega t\right)}{dt}$

$\epsilon =-AB\omega (-\sin \omega t)N$

$\epsilon =NAB\omega \sin \omega t$

$\omega =2\pi f$

$\epsilon =2\pi fNAB\sin \omega t$

${\epsilon }_{max}=2\pi fNAB$

${\epsilon }_{max}=2\times 3.14\times 60\times (20\times 10\times {10}^{-4})\times 0.5\times 30$

${\epsilon }_{max}=113.04volt$

Hence, the maximum induced emf is $113.04volt$