Ch. 22 Electromagnetic Waves

James Clerk Maxwell

From his studies on electromagnetic induction, Maxwell realized: “Accelerating Charges give rise to Electromagnetic Waves” Maxwell's equations demonstrate that electricity, magnetism and light are all manifestations of the same phenomenon, namely the electromagnetic field.

Units of Chapter 22

• Changing Electric Fields Produce Magnetic Fields; Maxwell’s Equations

• Production of Electromagnetic Waves

• Light as an Electromagnetic Wave and the Electromagnetic Spectrum

• Measuring the Speed of Light

• Energy in EM Waves

• Momentum Transfer and Radiation Pressure

• Radio and Television; Wireless Communication

22.1 Changing Electric Fields Produce Magnetic Fields; Maxwell’s Equations

Maxwell’s equations are the basic equations of electromagnetism. They involve calculus; here is a summary:

1. Gauss’s law relates electric field to charge

2. A law stating there are no magnetic “charges”

3. A changing electric field produces a magnetic field

4. A magnetic field is produced by an electric current, and also by a changing electric field

22.2 Production of Electromagnetic Waves A changing electric field

produces a magnetic field

And

A changing magnetic field

produces an electric field

Once sinusoidal fields are created they can propagate on their own.

These propagating fields are called electromagnetic waves.

22.2 Production of Electromagnetic Waves

This is the speed of light in a vacuum.

Maxwell invented the field called “Dimensional Analysis”

Realized that the ratio of Electric to Magnetic Field had the dimensions of a velocity (m/s), and this term appeared in an expression for the velocity at which EM waves should travel

E = v = c B

22.2 Production of Electromagnetic Waves Oscillating charges will produce electromagnetic waves

Far from the source, the waves are plane waves

22.2 Production of Electromagnetic Waves The electric and magnetic waves are perpendicular to each other, and to the direction of propagation.

22.3 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

Light was known to be a wave, and experiments demonstrated that EM waves share all of the same behaviors.

The frequency of an electromagnetic wave is related to its wavelength:

c = 3x108 m/s

This wave-speed equation is the same one that applies to sound, and any other waves.

A few years after Maxwell’s breakthrough, Tesla invented (and patented) radio technology (1897)

Marconi commercialized it and Wireless communication revolutionized the world within a few short years. (First TransAt: 1901)

Electromagnetic waves can have any wavelength; we have given different names to different parts of the wavelength spectrum.

Electromagnetic Spectrum

22.4 Measuring the Speed of Light

The speed of light was known to be very large, although careful studies of the orbits of Jupiter’s moons showed that it is finite.

One important measurement, by Michelson, used a rotating mirror:

Measuring the Speed of Light

Over the years, measurements have become more and more precise; now the speed of light is defined to be:

This is then used to create a stable definition for the meter.

22.7 Radio, TV, Wireless Communication

This figure illustrates the process by which a radio station transmits information. The audio signal is combined with a carrier wave:

•Remember those Capacitor “Time Constants” ?

•Radio Transmitters contain a special circuit containing a coil and a capacitor, designed to “oscillate” at kHz - MHz frequencies.

•This circuit creates the carrier wave.

•The audio signal is added by simply connecting the microphone output into the circuit.

Amplitude Modulation The mixing of signal and carrier can be done two ways. First, by using the signal to modify the amplitude of the carrier (AM):

Note the audio signal is only approximated by the AM envelope. The closer together the carrier “peaks” the more faithfully the signal can be reproduced.

FM - Frequency Modulation Second, by using the signal to modify the frequency of the carrier (FM):

FM results in much better signal reproduction, partly because the signal strength is constant, and partly because it is achieved at higher frequencies (more bits of information per second)

At the receiving end, the wave is received, demodulated, amplified, and sent to a loudspeaker:

The receiving antenna is bathed in waves of many frequencies; a tuner is used to select the desired one:

Why use a carrier wave at all? -Why not just broadcast the raw audio signal as an electromagnetic wave?

•To reduce the wavelength for efficient transmission and reception (the optimum antenna size is ½ or ¼ of a wavelength).

•A typical audio frequency of 3000 Hz will have a wavelength of 100 km and So would need an effective antenna length of 25 km! (this goes for both reception and transmission)

• By comparison, a typical carrier for FM is 100 MHz, with a wavelength of 3m, and could use an antenna only 80 cm long.

•The energy Density in very long wavelength wave is so small that interference would be overwhelming.

•Long wavelengths do not behave in a very directional way (which for certain very specialized applications is extremely useful)

•Digital Radio is even more efficient than FM, it uses a very high frequency, and basically switches the signal on and off rapidly to transmit 1’s and zero’s. Many more stations can occupy the the radio spectrum

Summary of Chapter 22

• Maxwell’s equations are the basic equations of electromagnetism

• Electromagnetic waves are produced by accelerating charges; the propagation speed is given by:

• The fields are perpendicular to each other and to the direction of propagation.

The simplest radio consists of something to rectify the signal (a diode in this case), and a tiny speaker

A Diode is a one-way valve for electric current. It isolates the positive side of the radio waveform.

Diodes today use germanium or silicon (semiconductors)

In the past Galena crystals were used, Even rusty razor blades and pencil leads can do the job in a pinch

Diode

Earpiece