Question

Prakash peddles a stationary bicycle, the pedals of which are attached to a $100$ turn coil of area $0.1m^2$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01T$ perpendicular to the axis of rotation of the coil. Determine the maximum voltage generated in the coil.

Answer 1

$N=100$

$A=0.1m^2$

$f=0.5$ rps i.e., $0.5$Hz

$B=0.01$T

Eind$=\frac{-db}{dt}=\frac{-d\left(NBA\cos \omega t\right)}{dt}$

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

$=NBA\omega \sin \omega t$

$(Eind{)}_{max}=NBA\omega$ i.e., if $\sin \omega t=1$

$\omega =2\pi f$

$\therefore (Eind{)}_{max}=NBA(2\pi f)$

$=\left(100\right)\left(0.01\right)\left(0.1\right)\left(2\pi \right)\left(0.5\right)$

$(Eind{)}_{max}=0.314$v.