Question

A flat circular coil of 1 cm radius is rotated at 10 revolutions per second about an axis that is perpendicular to a uniform magnetic field of magnitude 2.5 T. How many turns are required in the coil to generate a peak voltage of 750 mV? Group of answer choices 2 turns 5 turns 8 turns 15 turns 20 turns

Answer 1

emf induced, $\varepsilon_{max} = NBA \omega = NB* \pi r^2*2 \pi f = 2 \pi^2 fNBr^2$

Number of turns, $N = \frac{\varepsilon_{max}}{2 \pi^2 f Br^2}$

$\Rightarrow N = \frac{750* 10^{-3}}{2 \pi^2 *10 *2.5*0.01^2} \approx 15$

15 turns