Answers
Faraday's Law of Induction
Problem 1
Given: A circular loop of wire, 9.6 cm in diameter, in a magnetic field of 1.10 T. The loop, perpendicular to the field, is removed from the field in 0.15 s.
Find: The average induced emf
-DFB/Dt
And the definition of the flux: FB/Dt = BAcosq = BA since the field is perpendicular to the loop
We arrive at
E = ADB//Dt Find the area, change in B and t are given
Problem 2
Given: A coil of wire, diameter 10.2 cm is oriented so that its plane is perpendicular to a magnetic field of 0.63 T. The magnetic field is pointing up.
In a period of 0.15 seconds, the field is changed to an orientation so that it is pointing down with a strength o 0.25 T.
Find: The average induced emf in the coil.
Using up as the positive direction
-DFB/Dt Find the area. The change in the field can be calculated from the information given
Generators
Problem 3
Given: A car is idling at 1100 rpm (revolutions per minute) and its generator is producing 12.4 volts
Find: The output if the rotation speed is increased to 2500 rpm. Assume nothing else changes.
We use the generator equation, equation 21-5
E = NB wAsinwt
Where, assuming the coil is rotating with constant angular velocity (otherwise, E = 2NBlvsinq as explained in the text
E = induced voltage, N = number of loops in the coil, omega = angular velocity, A is area, and t is time
Since the induced voltage is proportional to the angular speed, their quotient is constant.
E1/w2 = E2/w2 ð E2 = E1/w2/w1
Transformers
Problem 4
Given: A transformer has 164 turns in the primary coil. It is designed to change 120 V into 10,000 V.
Find: The number of turns in the secondary coil
Vs/Vp = Ns/Np ð Ns = Np(Vs/Vp)