3P32-

Recall Electromagnetic Radiation: Plane Waves

http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/07-EBlight/07-EB_Light_320.html

4P32-

Properties of EM Waves

8

0 0

1 3 10 mv csµ ε

= = = ×

0

0

EE cB B= =

Travel (through vacuum) with speed of light

At every point in the wave and any instant of time, E and B are in phase with one another, with

E and B fields perpendicular to one another, and to the direction of propagation (they are transverse):

Direction of propagation = Direction of ×E B

6P32-

Shake A Sheet of Charge Up and Down

7P32-

Java Applet for Generation of Plane Waves

http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/09-planewaveapp/09-planewaveapp320.html

8P32-

First Pull The Sheet of Charge Down At Speed v

1

0

tan E vT vE cT c

θ = = =

1 00

ˆ ˆ2

v vEc c

σε

⎛ ⎞⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

E j j

When you pull down, there is a back force up!

9P32-

Rate of Work Done?2

10 0

ˆ ˆ( )2 2ev v dAd dq dAc c

σ σσε ε

⎛ ⎞ ⎛ ⎞= = =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠F E j j

2

ext0

ˆ2ev dAd d

cσε

⎛ ⎞= − = −⎜ ⎟

⎝ ⎠F F j

( )2 2 2 2

ext ext

0 0

ˆ ˆ2 2

d W d d v vvdAdt dA dt c c

σ σε ε

⎛ ⎞= ⋅ = − ⋅ − =⎜ ⎟

⎝ ⎠

F s j j

10P32-

What About B Field?

01

0

ˆ( 2) , 0

ˆ( 2) , 0

v x

v x

µ σ

µ σ

⎧+ >⎪= ⎨− <⎪⎩

kB

k1 0

0

ˆ ˆ2

v vEc c

σε

⎛ ⎞⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

E j j

11P32-

Rate Energy Carried Away?

2 20

1 10 0 0 0

1 1 ˆ ˆˆ2 2 4

vv vc c

µ σσ σµ µ ε ε

⎛ ⎞ ⎛ ⎞⎛ ⎞= × = × =⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

S E B j k i

Energy radiated to left and right is exactly equal to the rate of work required to move sheet down

12P32-

To generate plane wave, move sheet up and down sinusoidally

The work you do in moving the sheet is carried away as electromagnetic radiation, with 100% efficiency.

13P32-

Generating Plane Wave Applet

16P32-

Generating Electric Dipole Radiation Applet

17P32-

Quarter-Wavelength AntennaAccelerated charges are the source of EM waves. Most common example: Electric Dipole Radiation.

4λ

4λ

t = 0 t = T/4 t = T/2 t = T

18P32-

Why are Radio Towers Tall?AM Radio stations have frequencies 535 – 1605 kHz. WLW 700 Cincinnati is at 700 kHz.

8

3

3 10 m/s 429 m700 10 Hz

/ 4 107m 350ft

cf

λ

λ

×= = =

×≈ ≈

The WLW 700 Cincinnati Tower is 747 ft tall

19P32-

Quarter-Wavelength Antenna

20P32-

Quarter-Wavelength Antenna

http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/04-QuarterWaveAntenna/04-MicrowaveDLICS_320.html

21P32-

Spark Gap Transmitter

23P32-

Group Problem: Lumped LC Circuit

Height (into page): h

Parallel Plate

Capacitor

Cylindrical Inductor

Question: What is the resonance frequency?

Recall:

01LC

ω =0ACdε

= LIΦ

=

[ ]solenoid current per unit lengthoB µ=

24P32-

Our spark gap antenna

6 12 4(4.5 10 )(33 10 F) 1.5 10 sτ RC − −= = × Ω × = ×

rad1

4cf

T l= =

103 10 cm/s12.4cm×

=

92.4 10 Hz 2.4GHz= × =

1) Charge gap (RC)

2) Breakdown! (LC)

3) Repeat

25P32-

Spark Gap Transmitter

27P32-

Spark Gap Antenna

http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/03-AntennaPattern/03-MicrowaveAntenna_320.html

28P32-

Spark Gap Antenna

32P32-

Polarization of TV EM Waves

Why oriented as shown?

Why different lengths?