Four Chapter 7

Electromagnetic Waves

• We have seen so far that
  • A current carrying wire produces a magnetic field around it.
  • A conductor moving in a magnetic field has a current induced in it (or A conductor in a changing magnetic field has a current induced in it.).
• These two principles are responsible for many technological devices such as motors, generators, galvanometers, relays, and bells etc.
• Maxwell realized that these two principles were just specific circumstances of more general principles.
• These two principles applied to matter interacting with electric and magnetic fields. He generalized these to include situations where we have space free of all matter.
• To generalize these principles, he added two more
  • A changing electric field in space produces around it in a plane perpendicular to it, a magnetic field which is also changing with time.
    • The magnitude of the magnetic field is proportional to the rate of change of the electric field.
  • A changing magnetic field in space produces around it in a plane perpendicular to it, an electric field which is also changing with time
    • The magnitude of the electric field is proportional to the rate of change of the magnetic field
• Maxwell also realized that
  • the distribution of an electric charge in space, is related to the electric field it produces.
  • Magnetic lines are continuous and do not begin and end.
  • electric lines begin and end on charges.
• The two points maxwell added, led him to predict that changing magnetic or electric fields in one place cause an unending sequence of changes that propagate through space as an electromagnetic disturbance.
• Electromagnetic Wave - A disturbance that moves through space as fluctuating electric and magnetic fields.
  • A changing magnetic field in one place produces around it a changing electric field.
  • The changing electric field around the changing magnetic field produces a second changing magnetic field around the changing electric field.
  • The second changing magnetic field produces around it a second changing magnetic field which produces another changing electric field and so on.
  • We could just as easily started with a changing electric field to produce the same effect.

Hertz Experiment

• The first proof of the existence of electromagnetic wave came from Hertz's experiment.

• An apparatus similar to the one illustrated was used. A high voltage power source caused sparks to oscillate across the gap as shown. Each visible spark is actually a series of many small sparks, jumping rapidly back and forth (oscillating) between the terminals.
• The size of the metal plates attached to the spheres from which the sparks are produced, controls the frequency of the sparks produced.
• A loop of wire held near the oscillating spark, had a spark jump across the air gap between the ends of the wire whenever a spark jumped across the high voltage (induction coil) spark gap.
• Hertz reasoned that as the spark jumps back and forth across the gap of the induction coil, it must set up rapidly changing electric and magnetic fields. According to Maxwell's theory, these changes propagate through space as electromagnetic waves. Upon arrival at the loop of wire, the changing electric and magnetic fields produce a potential difference across the ends of the wire loop. If the potential is large enough, a spark jumps across the gap.
• The wave produced has the same frequency as the sparks. This frequency was about 1.0 X 10⁹ Hz.
• Hertz showed that the speed of the waves were 3.00 X 10⁸ m/s.
• Hertz also showed that these waves had many of the usual properties of light.
• Maxwell predicted the properties of electromagnetic waves.
  • Produced whenever electric charges are accelerated
    • accelerating charges lose energy which is carried away as electromagnetic waves
  • If an electric charge is accelerated in a periodic fashion, the frequency of the electromagnetic waves equals the frequency of the oscillations of the charge.
  • All electromagnetic waves travel in a vacuum at 3.00 X 10⁸ m/s, and obey the universal wave equation.
  • Electromagnetic waves exhibit:
    • interference, diffraction, polarization, refraction, etc.
    • linear and angular momentum.
    • Intensities proportional to the square of the magnitude of the electric (or magnetic) field amplitude, and to the square of the frequency.
  • Electromagnetic waves consist of oscillating electric and magnetic fields in a constant phase relation perpendicular to each other and perpendicular to the direction of propagation as illustrated below.
    • Notice how the right hand rule applies to this diagram. Point your fingers in the direction of motion of the wave. Twist your arm so that you can curl your fingers into the direction of the electric field. Your thumb points in the direction of the magnetic field.

• Hertz called the waves radio waves
• People like Marconi used these waves to build the first radios.
• The velocity of electromagnetic waves is given by