Question

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 10.4 cm2cm2 is rotated in a time interval of 3.20×10⁻² ss from a position where its plane is perpendicular to the earth's magnetic field to one where its plane is parallel to the field. The earth's magnetic field at the lab location is 7.0×10⁻⁵ T

A)What is the magnetic flux through each turn of the coil before it is rotated?

B)What is the magnetic flux through each turn of the coil after it is rotated?

C)What is the average emf induced in the coil?

Answer 1

(a) Magnetic flux linked with each turn of the coil before it is rotated is given by

$\phi$i =  BA cos$\theta$i = (7*10-5*10.4*10-4*cos 0o) weber

= 72.8*10-9 Wb

Where, $\theta$ i is the angle between the magnetic field and area vector of the coil.

Direction of area vector is perpendicular to the plane of the coil.

(b) Similarly, magnetic flux linked with each turn of the coil after the rotation

$\phi$f = BA cos$\theta$f = (7*10-5*10.4*10-4*cos 90o) Wb

= 0 Wb

As, cos 90o = 0, here, $\phi$ f is the angle between the magnetic field and the area of the coil after rotation.

(c) Now, induced emf is given by

00 E = -1 at

Where, N = number of turns = 200

$\partial \phi$ = Change in glux = (0 - 72.8/10-9) Wb

= - 72.8*10-9 Wb

$\partial t$ = time interval = 3.2*10-2 sec

Thus, emf = - 200*(-72.8*10-9/3.2*10-2) volt

= 455*10-6 volt