Dynamic Fields and Waves

A Norton

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9780429530388
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This book explores the use of waves on strings and sound waves to illustrate the behaviour of waves. It shows how Albert Einstein overturned Newtonian physics and predicted startling new effects such as time dilation and length contraction for objects travelling at close to the speed of light.

Chapter 1 Fields that vary with time

1 Current without wires—some examples of induction

Figure 1.1 shows two sealed boxes. One of the boxes has a light bulb holder set into it, with a bulb in place. It is like an ordinary lamp, except that there are no wires connecting it to the domestic electricity supply. The second box has a wire coming out of it, ending in a plug, which is attached to a wall socket. The two boxes are separated by a distance of about a centimetre. When the current is switched on at the socket, the bulb glows, and continues to do so as long as the current continues to flow through the other box. If you were to pass your hand between the two boxes you would feel nothing, and the light from the bulb would not change.

Figure 1.1 A wireless lamp.

How can the bulb light up with no supply of electricity to it? You may think that you have been fooled. Is there a battery inside the box with the bulb? However, as Figure 1.2 shows, all that is inside each box is a coil of insulated copper wire wound around a cylindrical core of iron — a solenoid. In Static fields and potentials you met solenoids as devices that use electric current to produce a magnetic field. In this chapter you will learn how an effect called electromagnetic induction allows a current flowing in one solenoid to ‘induce’ a current in a second solenoid and thus cause the bulb in the other box to glow.

Now consider something quite different. Suppose you want to melt a small piece of brass or steel, perhaps as part of some jewellery you are making. The melting temperatures of these metals are so high that it is difficult to melt them by direct heating. The standard method of melting uses an induction furnace, similar to that shown in Figure 1.3a. Superficially, this consists of a box with a hinged door, inside which is a ceramic crucible. A wire leads from the box to an electricity supply. The metal is placed in the crucible, the door is closed, the switch is thrown to complete the circuit, and after a while the metal melts. Taking apart the box to see how it works (Figure 1.3b), you would discover a solenoid encircling the crucible. (The solenoid is contained in a water jacket to keep it from overheating.)

Figure 1.2 Inside view of a wireless lamp.

Figure 1.3 (a) An induction furnace; (b) diagrammatic view of the interior of an induction furnace.

Both the wireless lamp and the induction furnace involve solenoids and therefore magnetic fields. However, the essential common ingredient is that in both cases the current flowing through those solenoids is not constant. Rather, it varies with time and, consequently, so does the magnetic field that each solenoid produces.

Stated simply, electromagnetic induction is the effect whereby changing magnetic fields cause, or ‘induce’, currents. Since fields are involved, these currents can be induced over distances without intervening wires. It is this principle that enables electric razors, food processors, vacuum cleaners, doorbells, washing machines, radios, televisions, telephones, and a host of other devices to work (Figure 1.4). Electromagnetic induction, or just induction for short, is the principal theme of this chapter. In it you will see how currents and magnetic fields which change in time affect each other, and how the devices described above are ingenious arrangements for harnessing these effects for useful purposes.

Figure 1.4 Many everyday devices rely on the principle of electromagnetic induction.

The last part of this chapter will take a new direction. It concerns the work of James Clerk Maxwell, who discovered that electric and magnetic fields can conspire together to create wave-like disturbances that travel at the same speed as that of light. This led to the acceptance that light itself is an electromagnetic wave. This unification of light and optics with electricity and magnetism ranks as one of the major discoveries of science, and is a high-water mark of nineteenth-century physics. It will be further discussed in Chapter 2 of this book.

2 Principles of electromagnetic induction

To set the stage for the discussion, you should recall Oersted’s discovery (Static fields and potentials Chapter 4), in 1820, that an electric current can affect a magnetic compass. For the first time there was an effect linking electricity and magnetism: electric currents create magnetic fields. Until this time, electricity and magnetism were thought to be entirely separate phenomena.

If an electric current can create a magnetic field, it seems quite reasonable to ask if magnetic fields will have any influence on electric currents. This was the problem that Michael Faraday set himself to solve, though at first with no success.

Michael Faraday (1791–1867)

Michael Faraday (Figure 1.5) was raised in humble circumstances, and received only a rudimentary education. He did, however, learn to read, and when he was later apprenticed to a bookbinder, Faraday took the opportunity to read some of the books that were brought in for binding. By 1813, this interest led him to a job at the Royal Institution, where he remained for the rest of his life. He founded the Royal Institution Christmas Lectures for children in 1826, and gave the lectures himself 19 times.

Faraday worked on the problem of electromagnetic induction from at least the time of Oer...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Introduction
• Chapter 1 Fields that vary with time
• Chapter 2 Waves and electromagnetic radiation
• Chapter 3 Optics and optical instruments
• Chapter 4 Special relativity
• Chapter 5 Consolidation and skills development
• Answers and comments
• Acknowledgements
• Index