VISUAL PHYSICS ONLINE

6 ELECTROMAGNETISM

P60 017

Consider the generator shown in the diagram with the parameters

magnetic field B = 1.25 T

L_CD = L_EF = 12 mm L_DE = L_CF = 6.0 mm

Rotation rate = 20 rpm (revolutions per minute)

Number of turns of coil N = 100

Total resistance of coil R_coil = 10 W

Resistance of external load connected between A and B R_load = 125 W

(A) Calculate:

Angular frequency w = ? rad.s^-1

Frequency of rotation f = ? Hz

Period of rotation T = ? s

Maximum magnetic flux f_B = ? T.m²

Maximum induced emf (polarity of point A w.r.t to the point B) emf = ? V

Maximum induced current in the circuit I = ? A

(B) Sketch the time graphs for the quantities: magnetic flux; induced emf; induced current.

(C) On your graphs add curves to show the resulting changes that would occur if the rotation speed was doubled.

The generator is now to be used a motor. The coil is no longer rotated by an external mechanical energy supply and the load is removed from between A and B.

The point A was connected to the positive terminal of a 12 V battery and point B was connected to the negative terminal.

(D) Explain why this arrangement does not work as a motor.

(E) The commutator of the slip rings is replaced by a split ring. The motor now works. Why?

View solution below only after you have completed the answering the question.

Solution

L_CD = L_EF = 12 mm = 12´10^-3 m L_DE = L_CF = 6.0 mm = 6´10^-3 m

Magnetic field B = 1.25 T

Rotation rate = 20 rpm (revolutions per minute)

Number of turns of coil N = 100

Total resistance of coil R_coil = 10 W

Resistance of external load connected between A and B R_load = 125 W

(A)

w = 20 rpm = (20)(2p) / (60) rad.s^-1 = 2.09 rad.s^-1

area of coil rotating in magnetic field A = (12´10^-3) (6´10^-3 m) = 72x10^-6 m²

R_total = R_coil + R_load = (10 + 125) W = 135 W

(B) (C)

As rotation rate increase Þ increase in induced emf Þ increase in current Þ greater force opposing rotation of coil Þ counter torque

(D) (E)