Electromagnetic Waves

1. Electromagnetic Waves Unit 9

2. Where we are… • We will finish the 3rd quarter with a general study of electromagnetic waves. • When we return from break, we will begin our study of optics. • There will be a daily exercise quiz on Friday. • There will be a unit quest next Friday. • Your essay rough drafts are due next Friday.

3. Maxwell’s Equations • When James Clerk Maxwell began his work in the 1860’s, there was some evidence of a relationship between electricity and magnetism. • For example, it was known that electric currents produce magnetic fields. • However, the two were considered to be separate subjects.

4. Maxwell’s Equations • Maxwell showed that all the phenomena of electricity and magnetism can be described using only 4(!) equations. • These equations are fundamental laws of nature like Newton’s laws of motion. • They are actually more fundamental since they are also consistent with Relativity.

5. Maxwell’s Equations • Gauss’s Law: Electric field lines start on positive charges and end on negative charges. The strength of the field depends on the amount of charge within a closed region of space. • Gauss’s Law for Magnetism: Magnetic field lines neither begin nor end. They form closed loops.

6. Maxwell’s Equations • Faraday’s Law: A changing magnetic field generates an electric field. • Ampere’s Law with Maxwell’s Correction: Magnetic fields are generated by electric currents or by a changing electric field. • Equation 4 contains Maxwell’s great insight: a changing electric field produces a magnetic field.

7. Maxwell’s Equations

8. Electromagnetic Waves • Let’s examine Maxwell’s insight more closely. • According to Maxwell, a magnetic field will be produced in empty space if there is a changing electric field. • But, the strength of the B field varies with the E field. So, the B field is also changing.

9. Electromagnetic Waves • But changing B fields generate E fields (Faraday’s Law). • So the B field produces its own E field, which is also changing in time. • As a result, the original changing E field produces a wave of changing E and B fields that travel through space. • These are electromagnetic waves.

10. Electromagnetic Waves • Consider the following system for generating EM waves. • Two pieces of metal are connected to opposite ends of a battery. • The switch is initially open.

11. Electromagnetic Waves • When the switch is closed, the the battery creates a potential difference. • The top rod becomes positively charged and the bottom rod becomes negatively charged. • While this rearrangement is occurring, there is a current flowing in the direction indicated.

12. Electromagnetic Waves • As a result of the current, a magnetic field is generated near the rods. • These magnetic fields vanish quickly near the source. • However, they generate E fields further away, which generate more B fields.

13. Electromagnetic Waves • The result is a wave pulse that travels away from the source. • There is also a static E field due to the charge arrangement. • This is unrelated to the wave propagation.

14. Electromagnetic Waves • Now let’s consider what happens if we connect the rods to an AC source. • In this case, the direction of the current is continually changing direction.

15. Electromagnetic Waves • When the current is running up, the E and B fields are a shown. • When the current switches to pointing down, opposite fields are generated. • However, the old fields do not disappear.

16. Electromagnetic Waves • Instead, the E field lines fold back on themselves to form closed loops. • This region of E and B fields no longer depends on the antenna and continues to travel out into space.

17. Electromagnetic Waves • The E and B fields near the antenna are referred to as the near field. • These fields are complicated and we will not be concerned with them. • The fields far away from the antenna are called the radiation field.

18. Characteristics of EM Waves • EM waves have several important characteristics. • EM waves are spherical. They propagate out in all directions.

19. Characteristics of EM Waves • As with all spherical waves, the field lines become very flat far from the source. • At this point, the wave is referred to as a plane wave.

20. Characteristics of EM Waves • Second, notice that at every point the electric and magnetic fields are perpendicular to each other and to the direction the wave is traveling.

21. Characteristics of EM Waves • Based on these facts, we can see that the fields vary from a maximum in one direction, to zero, to a maximum in the other direction. • The E and B fields are also in phase. The reach their maximums at the same time and are zero at the same time.

22. Characteristics of EM Waves • If the source voltage changes sinusoidally, then so will the E and B fields. • Animation!

23. Characteristics of EM Waves • Based on this, it is easy to see that EM waves are transverse waves. • Note that they are oscillations in the E and B fields, not matter.

24. Characteristics of EM Waves • We have also seen that waves are created by electric charges that are oscillating. • In order to oscillate, these charges must be accelerating.

25. Characteristics of EM Waves • This leads us to an important conclusion: Accelerating electric charges give rise to electromagnetic waves.

26. Speed of EM Waves • Maxwell was also able to calculate the speed an electromagnetic wave travels at:

27. Speed of EM Waves • He was also able to show that the speed could be calculated using physical constants.

28. Speed of EM Waves • If we plug in for these values, we get the speed is • This turns out to be exactly equal to the measured speed of light.

29. Questions • If light travels at the same speed as EM waves, what does that imply about the nature of light? • The speed of light does not specify what it is measured relative to. Why is this problematic?

30. Homework • Read sections 22-1 and 22-2. • Work on your paper.

31. Light and the Electromagnetic Spectrum

32. The EM Spectrum • Maxwell’s equations produced two startling results: • The existence of electromagnetic waves • Electromagnetic waves travel at the speed of light • Light had been known to have wave properties. • However, it was not known what was oscillating in a light wave. • Maxwell argued that light must be an EM wave.

33. The EM Spectrum • Since EM waves (including light) are wave phenomena, they have both a frequency and a wavelength. • As with previous wave phenomena we have studied, the frequency and wavelength are related to the speed of the wave by

34. Light • The wavelengths of light were measured long before light was thought to be an EM wave. • The wavelengths range from 4.0 x 10-7 m and 7.5 x 10-7m. • Because these wavelengths are so small, they are usually reported in nanometers (nm). • Using these units, the wavelengths of light range from 400 nm to 750 nm.

35. The EM Spectrum • But light is only one kind of EM wave. • There are many other possible frequencies. • This range of waves is known as the electromagnetic spectrum.

36. The EM Spectrum • The first electromagnetic waves generated in the lab had a frequency of roughly 109 Hz. • Today, we refer to these as radio waves. • Radio waves are the lowest frequency EM waves.

37. The EM Spectrum • Microwaves are EM waves of higher frequency. • Above microwaves are infrared (IR) light. • IR waves from the sun is primarily responsible for the sun’s warming effect.

38. The EM Spectrum • Above the violet end of the visible spectrum is the ultraviolet(UV) range. • UV light from the sun can cause skin damage with prolonged exposure.

39. The EM Spectrum • Above the UV range are X-rays. • X-rays are generally produced with electrons strike a metal target and are rapidly decelerated. • X-rays have a very high frequency and can be very damaging to human tissue.

40. The EM Spectrum • The highest frequency waves are known as Gamma rays. • Gamma rays are produced through natural processes, or through the collision of fast-moving atoms in a particle accelerator.

41. Example: Wavelengths of EM Waves Calculate the wavelength of a) a 60 Hz EM wave. b) a 91.5 Hz FM radio wave. c) a beam of 4.74 x 1014 Hz red light from a laser pointer. d) a dental X-ray with a frequency of 5 x 1018 Hz.

42. Homework • Read section 22-3. • Do problems 5, 7, 9, and 10 on pages 629-630.

43. Measuring the Speed of Light

44. Galileo • Galileo was the first to attempt a measurement of c. • He tried to measure the time it took light to travel between two hilltops. • If he knew the spacing of the hills and could measure the time, he could figure out c.

45. Galileo • In the experiment, Galileo stood on the top of one hill with a covered lamp. • His assistant stood on the top of the other hill with a lamp that was also covered.

46. Galileo • Galileo would open the cover on his lamp, causing the light to travel toward his assistant. • Once the assistant saw the light from Galileo’s lamp, he would open the cover on his lamp. • Galileo would then measure the time between the moment he opened the first lamp and the instant he saw the light from his assistant’s lamp.

47. Galileo • Although Galileo’s method was sound, light travels so fast that the time Galileo measured was extremely short. • It was so short that it could not be distinguished from human reaction time. • Galileo could only conclude that the speed of light was very high.

48. Michelson • One of the first scientists to successfully measure c was Albert Michelson. • From 1880 to the early 1920s, he conducted a series of high-precision experiments to measure the speed of light.

49. Michelson • In the experiment, light from a source was directed at an eight-sided rotating mirror. • The mirror reflected the light to a stationary mirror a large distance away.

50. Michelson • The stationary mirror reflected the light back to the rotating mirror. • The light would then be reflected depending on what point the mirror was at in its rotation.