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,

Electromagnetic Waves

Unit 9

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.

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 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.


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 Equations3. 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.



• 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.


• 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.


• 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.


• 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.


• 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.


• 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.


• 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.


• 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.


• 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.


• 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.


• 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.


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


• 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.


• If the source voltage changes sinusoidally, then so will the E and B fields.

• Animation!

http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html


• 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.


• We have also seen that waves are created by electric charges that are oscillating.

• In order to oscillate, these charges must be accelerating.


• 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 22-2.

• 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 10-7 m and 7.5 x 10-7 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 109 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 ofa) 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.

Homework

• Read section 22-3.

• Do problems 5, 7, 9, and 10 on pages 629-630.

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 22-7.

• Do problems 12, 13, 16, 17, and 27 on page 630.

Documents

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,