Question

Faraday’s Law

(4) A 75 turn rectangular coil of height 5.40 cm and width 3.40 cm rotates about a perpendicular axis in a uniform magnetic field of 825 mT. The maximum emf induced in the coil is 6.25 V.

(a) Find the maximum magnetic flux through the coil.

(b) Find the coil’s angular velocity in revolutions per minute.

(c) Sketch the magnetic flux through the coil, and the induced emf, as a function of time.

Answer 1

Part a

flux through the coil

$\phi = NBA cos(\theta)$

maximum magnetic flux

$\phi_m = NBA$

$\phi_m = (75)(0.825)(0.054\times 0.034)$

$\phi_m = 0.114 W$

part b

induced emf is given as

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

$\epsilon =NBA\omega sin(\theta)$

maximum emf when so

90

$\epsilon =NBA\omega$

$6.25 =0.114\omega$

$\omega = 54.82 re/s$

$\omega = 3289.2 re/m$

part c

emf W t