Page 453 - Physics Coursebook 2015 (A level)

Chapter 28: Electromagnetic induction
QUESTIONS
6 In the type of generator found in a power station (Figure 28.15), a large electromagnet is made to rotate inside a fixed coil. An e.m.f. of 25 kV is generated; this is an alternating voltage of frequency 50 Hz. What factor determines the frequency? What factors do you think would affect the magnitude of the e.m.f.?
Figure 28.15 The generators of this power station produce electricity at an induced e.m.f. of 25 kV. For Question 6.
Faraday’s law of electromagnetic induction
Earlier in this chapter, we saw that electromagnetic induction occurs whenever a conductor cuts across lines of magnetic flux – for example, when a coil is rotated in a magnetic
field so that the magnetic flux linking the coil changes. We can use Faraday’s law of electromagnetic induction to determine the magnitude of the induced e.m.f. in a circuit:
We can write this mathematically as:
E ∝ Δ(NΦ) Δt
where Δ(NΦ) is the change in the flux linkage in a time Δt. Working in SI units, the constant of proportionality is equal to 1. Therefore:
E = Δ(NΦ) Δt
The equation above is a mathematical statement of Faraday’s law. Note that it allows us to calculate the magnitude of the induced e.m.f.; its direction is given by Lenz's law, which is explained in the next section on page 442.
7 A bar magnet produces a uniform flux density
of 0.15 T at the surface of its north pole. The pole measures 1.0 cm × 1.5 cm. Calculate the magnetic flux at this pole.
8 A solenoid has diameter 5.0 cm and length 25 cm (Figure 28.16). There are 200 turns of wire. A current of 2.0 A creates a magnetic field of flux density 2.0 × 10−5 T through the core of this solenoid. Calculate the magnetic flux linkage for this solenoid.
5.0 cm
Figure 28.16 A solenoid. For Question 8.
9 A rectangular coil, 5.0 cm × 7.5 cm, and having 120 turns, is at right angles to a magnetic field of flux density 1.2 T. Calculate the magnetic flux linkage for this coil.
Now look at Worked examples 2 and 3.
WORKED EXAMPLES
2 A straight wire of length 0.20 m moves at a steady speed of 3.0 m s−1 at right angles to a magnetic field of flux density 0.10 T. Use Faraday’s law to determine the e.m.f. induced across the ends of the wire.
Step1 Withasingleconductor,N=1.Todetermine the e.m.f. E, we need to find the rate of change
of magnetic flux; in other words, the change in magnetic flux per second.
25 cm
200 turns
The magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux linkage.
3.0 m s–1 0.20 m
3.0 m
Figure 28.17 A moving wire cuts across the magnetic field.
Figure 28.17 shows that, in 1.0 s, the wire travels 3.0 m. Therefore:
change in magnetic flux = B × change in area change in magnetic flux = 0.10 × (3.0 × 0.20)
=6.0×10−2Wb
B = 0.10 T
441