giambattista college physics chapter 22

Giambattista College Physics Chapter 22

Giambattista College Physics Chapter 22

©2020 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

©2020 McGraw-Hill Education

Chapter 22: Electromagnetic Waves

22.1 Maxwell’s Equations and Electromagnetic Waves.

22.2 Antennas.

22.3 The Electromagnetic Spectrum.

22.4 Speed of EM Waves in Vacuum and in Matter.

22.5 Characteristics of Traveling Electromagnetic Waves in Vacuum.

22.6 Energy Transport by EM Waves (a little...).

22.7 Polarization.

22.8 The Doppler Effect for EM Waves.


22.1 Maxwell’s Equations and Electromagnetic Waves

In our study of electromagnetism so far, we have considered the electric and magnetic fields due to charges whose accelerations are small.

A point charge at rest gives rise to an electric field only. A charge moving at constant velocity gives rise to both electric and magnetic fields.

Charges at rest or moving at constant velocity do not generate electromagnetic waves—waves that consist of oscillating electric and magnetic fields.


Accelerating Charges Produce Electromagnetic Waves

Electromagnetic (EM) waves are produced only by charges that accelerate.

EM waves, also called electromagnetic radiation, consist of oscillating electric and magnetic fields that travel away from the accelerating charges.

There are no electric waves or magnetic waves; there are only electromagnetic waves.


Maxwell’s Equations 1

Maxwell modified Ampère’s law and used it with the three other basic laws of electromagnetism to predict the existence of electromagnetic waves and to derive their properties.

His theory predicted that EM waves of any frequency travel through vacuum at the same speed, a speed that closely matched measurements of the speed of light—strong evidence that light is an EM wave.



In honor of Maxwell’s achievements, the four basic laws of electromagnetism are collectively called Maxwell’s equations. They are:

1. Gauss’s law [Eq. (16-17)]: If an electric field line is not a closed loop, it can only start and stop on electric charges. Electric charges produce electric fields.

2. Gauss’s law for magnetism: Magnetic field lines are always closed loops since there are no magnetic charges ( monopoles ). The magnetic flux through a closed surface (or the net number of field lines leaving the surface) is zero.



3. Faraday’s law [Eq. (20-18)]: Changing magnetic fields are another source of electric fields.

4. The Ampère-Maxwell law says that changing electric fields can be a source of magnetic fields. Now, electric AND magnetic field lines form closed loops.

5. NET EFFECT: I need charges to create electric and magnetic fields, but THEN the electric and magnetic fields can propagate on their own, each sustaining the other. And the fields can carry energy and momentum through space.



Recall that:

Electric fields are described by e0 (for example, this set the strength of the electric field in a capacitor)

Magnetic fields are described by m0 (for example, this set the strength of the magnetic field in a solenoid)

Maxwell showed that electromagnetic fields can propagate as a wave that moves at speed:

!! Do this calculation.

c=[ϵ 0 μ0]−1/2= 1

√ϵ 0 μ0≈3⋅108m / s


22.2 Antennas

The electric dipole antenna consists of two metal rods lined up as if they were a single long rod. The rods are fed from the center with an oscillating current.

For half of a cycle, the current flows upward; the top of the antenna acquires a positive charge and the bottom acquires an equal negative charge.


Electric Dipole Antenna as Transmitter 1

When the current reverses direction, these accumulated charges diminish and then reverse direction so that the top of the antenna becomes negatively charged and the bottom becomes positively charged.

When these charges reverse direction, they ACCELERATE, producing alternating electric and magnetic fields that can now propogate through space.

The result of feeding an alternating current to the antenna is an oscillating electric dipole.



This produces an electric (E) and magnetic (B) field perpendicular to each other, and BOTH perpendicular to the direction of the flow of energy(S): (A half-cycle later it looks like:)

B

E

S

BS

E


Electromagnetic waves

B

E

S

By SuperManu - Self, based on Image:Onde electromagnetique.png, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2107870



B

E

S

Lookang many thanks to Fu-Kwun Hwang and author of Easy Java Simulation = Francisco Esquembre, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons



B

E

S


lAt each instant, energy flows in the direction of the Poynting vector:

!! Show that the units of are power/area = Watt/m2

S⃗= E⃗×B⃗μ0

S⃗



B

E

S


lIn the time it takes the wave to oscillate once (the period, T) the wave MOVES a distance equal to the length of a wave (the wavelength :). So the speed of the wave is:

c=Δ xΔ t

=λT

=λ f


22.3 The Electromagnetic Spectrum

Access the text alternative for these images


Visible Light


Sunlight




EXAMPLE: The peak of sunlight is at a wavelength of about 500 nm. So the frequency is about:

This is INCREDIBLY fast – only an electron is light enough to accelerate enough to make an EM wave that oscillates at this frequency.

!! The WiFi antenna in your phone can emit EM waves at a frequency of 5GHz. What is the wavelength?

f= cλ ≈ 3⋅108m /s500⋅10−9m

=6⋅1014Hz=600THz



Compare the result to this picture of the Samsung Galaxy Note and identify the WiFi antenna.


Application: Microwave Oven



EXAMPLE: On the back of your microwave is a sticker that tells you the frequency of the “output” (the EM radiation inside when you turn it on). It should say 2450 MHz. The wavelength is then:

You can check this (google: “speed of light microwave cheese”)

!! At what frequency would an EM wave have a wavelength about as long as a human being? Where is this in the electromagnetic spectrum?

λ= cf≈ 3⋅108m/ s

2.45⋅109m=0.122m


Application: X-rays in Medicine and Dentistry, CT Scans


Example 22.2

A supernova is an exploding star; a supernova is billions of times brighter than an ordinary star. Most supernovae occur in distant galaxies and cannot be observed with the naked eye. The last two supernovae visible to the naked eye occurred in 1604 and 1987.

Supernova SN1987a occurred 1.6 × 1021 m from Earth. When did the explosion occur?


Example 22.2 Solution

2112

8

1.6 10 m5.33 10 s

3.00 10 m/s

dt

c

127

1 yr5.33 10 s 170000 yr

3.156 10 s

giambattista college physics chapter 22

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