Question

You take your trusty 120 turn solenoid, with 20 cm diameter and spin it at a rate of 10 times per second in a magnetic field that you have constructed with two gigantic neodymium magnets, creating a uniform magnetic field. You are spinning the solenoid so that its rotation axis is perpendicular to the magnetic field direction.

a) What field strength do you need to create a peak emf voltage of 150 V? (Hint: use flux as a function of angle.)

b) What orientation must the solenoid be in to achieve peak emf?

Answer 1

Flux, = NBA cos
Where N is the total number of turns, B is the field strength of neodymium magnet, A is the area of the solenoid and is the angle between B and A, for maximum flux, B and A must be in the same direction.
A = r²
= x (0.1)²
= 0.0314 m²
can be written as = t
Where is the angular frequency,
= 2f
= 2 x 10 = 62.83 rad/s

= NBA cos(t)
Induced emf = d/dt = - NBA sin(t)
For maximum emf, sin(t) = 1,
V = NBA
150 = 120 x B x 0.0314 x 62.83
= 236.87 B
B = 150/236.87
= 0.633 T

b)
For maximum emf, sin = 1,
For this, the solenoid must be perpendicular to the direction of magnetic field