Electromagnetic Waves Unit 9

Where we are… We will finish the 3 rd 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.

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.

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.

Maxwell’s Equations 1.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. 2.Gauss’s Law for Magnetism: Magnetic field lines neither begin nor end. They form closed loops.

Maxwell’s Equations 3.Faraday’s Law: A changing magnetic field generates an electric field. 4.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.

Maxwell’s Equations

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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.

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.

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

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

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

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.

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?

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

Light and the Electromagnetic Spectrum

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.

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

Light The wavelengths of light were measured long before light was thought to be an EM wave. The wavelengths range from 4.0 x m and 7.5 x m. 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.

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.

The EM Spectrum The first electromagnetic waves generated in the lab had a frequency of roughly 10 9 Hz. Today, we refer to these as radio waves. Radio waves are the lowest frequency EM waves.

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.

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.

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.

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.

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 Hz red light from a laser pointer. d) a dental X-ray with a frequency of 5 x Hz.

Homework Read section Do problems 5, 7, 9, and 10 on pages

Measuring the Speed of Light

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.

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.

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.

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.

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.

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.

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.

Michelson If the mirror was rotating too slowly or too quickly, the light would be deflected to the right or the left of the observer. However, if the mirror is rotating at just the right speed, the light will be reflected at the observer.

Michelson By knowing the distances of the setup and measuring the speed of the rotating mirror, Michelson was able to determine the speed of light.

Practice Review sections 22-4 and Do problems 12, 13, 16, 17, and 27 on page 630.