Using the formulae for periodic time of circular motion, area of a rectangle, magnetic flux and the induced emf in a solenoid, making sure all values are in their standard unit: Time taken for each revolution is:
T 2p v 2p
2p 0.25 s
During each revolution the area of each loop of the coil, through which the magnetic field passes, changes from ‘no area’, through ‘full area’, through ‘no area’ and ‘full area’ again and back to ‘no area’. This is a quarter of the periodic time of revolution; in this question it is 0.0625 s.
The area of each loop is: Area length width A (0.03)(0.04) 1.2 103 m2 When the magnetic field passes through the ‘full area’ the total flux is given by: BA (2.5)(1.2 103) 3 103Wb
Q
Therefore the time taken for flux to change from 0.3 Wb to 0 Wb every 0.0625 s: dt (200) 0.003
The induced emf is 9.6 V. E N d
0.0625 9.6
EXERCISE 20.2 ELECTROMAGNETIC INDUCTION
Q1 What is the magnetic flux cutting through a loop of area 0.2 m2 when it is positioned at right angles to a magnetic field of flux density 3.5 T?
Q2 A uniform magnetic field causes a magnetic flux of 3 Wb to pass through a circular loop of wire of diameter 50 cm. Calculate the magnetic flux density of the field.
Q3 What is the emf induced when the magnetic flux through a loop of wire changes from 6 Wb to 2 Wb in 0.2 s?
Q4 A circular loop of wire of radius 1.2 m enters a magnetic field of flux density 3 T travelling at 6 m s1, shown in Fig 20.27. Calculate: (i) the area of the circular loop (ii) the magnetic flux cutting the loop (iii) how long it takes for the loop to completely enter the field (iv) the average emf induced in the loop as it enters the magnetic field.
6 m s–1 1.2 m
++++++ ++++++ ++++++ ++++++
Magnetic field into page (a) Loop outside Fig 20.27 362 INVESTIGATING PHYSICS
