A single loop of area 0.193 m2 is placed perpendicular to a magnetic field of 0.374 T. The loop is rotated about an axis lying in the plane of the loop and passing through its center. An instantaneous emf of 9.21 Volts is generated when the plane of the loop makes an angle of 45 o with the field direction. What is the angular speed of the loop (rad/s)

The angular speed w of the loop = 181 rad/s

Explanation:

Given that;

Area A = 0.193 m2 

Magnetic field B = 0.374 T

E.m.f = 9.24v

Ø = 45 degree

According to Faraday's law when the magnetic flux linking a circuit changes, an electromotive force is induced in the circuit proportional to the rate of change of the flux linkage.

Using the formula

E.m.f = NABwcosØ

Where w = angular velocity.

Let assume that N = 1 then,

9.24 = 0.193 × 0.374 × w × cos45

9.24 = 0.051w

w = 9.24/0.051

w = 181 m/s

Therefore, the angular speed w of the loop = 181 rad/s