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Lecture 15.1 :Electromagnetic Waves

Lecture Outline:Electromagnetic Waves

Properties of Electromagnetic WavesPolarization

April 23, 2013

Textbook Reading:Ch. 34.5 - 34.7

Announcements

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•Quiz #6 on Thursday (34.1-34.5 material)

•Online Evaluation e-mails should be sent to you this week.

‣Please fill out the evaluation form...it is completely confidential. May 8 is deadline.

‣Remember that PHY212 and PHY222 (lab) are separate courses!

•Society of Physics Student (SPS) is planning to offer “clinic” services during Finals week. The regular clinic will also be open.

‣Date: May 1st

‣Time: 10am-4pm

‣Location: Rooms 104N and 106 in the Physics building.

‣Come with specific questions!

Last Lecture...

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Maxwell introduced the idea of a “displacement current”, which modifies Ampere’s Law. This current is due to

changing electric flux (such as in a charging capacitor).

��B · d�s = µ0

�Ithrough + �0

dΦe

dt

�

Idisp = �0dΦe

dt

Last Lecture...

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Maxwell’s Equations, plus Lorentz force law, form a complete theory of electromagnetism.

Last Lecture...

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Ey = E0sin (2π(x/λ− ft))

Bz = B0sin (2π(x/λ− ft))

E0 = vemB0

∂Ey

∂x= −∂Bz

∂tCondition on EM Waves

from Faraday’s Law

Electromagnetic Waves

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∂Bz

∂x= −�0µ0

∂Ey

∂tCondition on EM Waves

from Ampere-Maxwell Law

Electromagnetic Waves

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1

�0µ0vem= vem

E0 =B0

�0µ0vemE0 = vemB0

Electromagnetic Waves must travel at the Speed of Light!

vem wave =1

√�0µ0

≈ 3.0× 108m/s = c

We now have two relations on E0 and B0 that both need to be true.

Electromagnetic Waves

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Remember, electrogmagnetic waves do not just have to be visible light (wavelength ~ 100s of nanometers), but can be any wavelength.

Properties of Electromagnetic Waves

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Poynting vector, S, defines the flow of energy in an electromagnetic wave.

�S ≡ 1

µ0

�E × �B

S =EB

µ0=

E2

cµ0= c�0E

2

I =P

A= Savg =

c�02

E20

Average Intensity over one cycle

Clicker Question #1

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An electromagnetic plane wave is coming toward you, out of the screen. At one instant, the electric field looks as shown. Which is the wave’s magnetic field at this instant?

Eis in the direction of motion.

Clicker Question #2

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In which direction is this electromagnetic wave traveling?

A. Up.B. Down. C. Into the screen.D. Out of the screen.E. These are not allowable fields for an electromagnetic wave.

is in the direction of motion.

Properties of Electromagnetic Waves

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When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5E9 km from earth. It sent a signal with 21 W of power back to earth. Assuming the transmitter broadcast equally in all directions, what signal intensity was received one earth? What electric field amplitude was detected? What magnetic field amplitude was detected?

Properties of Electromagnetic Waves

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Electromagnetic waves exert a “radiation pressure” when they are incident on a surface.

Solar Sail

∆p =energy absorbed

c

prad =F

A=

P/A

c=

I

c

F =∆p

∆t=

(energy absorbed/∆t)

c=

P

c

Properties of Electromagnetic Waves

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Alternating current in an antenna creates an electromagnetic wave.

Properties of Electromagnetic Waves

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Polarization

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Plane defined by the Poynting vector and the Electric Field vector is called the Plane of Polarization.

Polarization

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Polarization

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Light reflecting off of a horizontal surface (such as a lake) has significant horizontal polarization.

Appropriate sunglasses can reduce the “glare”.

Which way are the “polymers” in your sunglasses oriented?

Polarization

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Itransmitted = I0cos2θ

Polarizer removes energy from the incident wave by diminishing it’s electric field amplitude.

Clicker Question #3

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Unpolarized light, traveling in the direction shown, is incident on polarizer 1. Does any light emerge from polarizer 3?

A. Yes.B. No.

Reminders

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•Quiz #6 on Thursday (34.1-34.5 material)•Don’t miss out on opportunities for Final exam

preparation (SPS “clinic”, regular “clinic”, review in class on Thu./Tue.).

•Final Exam is May 6th from 3-5pm.