Electromagnetic Waves Chapter 35. Electromagnetic (EM) Waves Can travel through space Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays All on the.

Electromagnetic Waves

Chapter 35

Electromagnetic (EM) Waves

• Can travel through space

• Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays

• All on the electromagnetic spectrum

James Clerk MaxwellMaxwell’s Equations

1. Guass’s Law – The greater the charge, the greater the electric field

2. Guass’s Law for magnetism - Magnetic flux is zero through a closed surface

3. Faraday’s Law – An electric field is produced by a changing magnetic field

4. Ampere-Maxwell Law - A magnetic field is produced by a changing electric field (moving charge)

Guass’s Law

Guass’s Law for magnetism

Faraday’s Law

Ampere-Maxwell Law

An electric field is produced by:

• Charged particle (moving or stationary)

• Changing magnetic field

A magnetic field is produced by:

• A curent (moving charge)

• Changing electric field

Lorentz Force

Results

• An electric field exerts a force on any charged particle

• A magnetic field exerts a force on a moving charged particle

Producing Electromagnetic Waves

DC case

• Current flows to either antenna (like a capacitor)

• Electric field produced

• Magnetic field produced (right hand rule)

AC case

• Changing direction of current

• Field line close up to form a loop

• Magnitude of E and B decrease with 1/r

• Energy is proportional to E2 or B2

EM Wave

• Sinusoidal

• E and B are perpendicular to one another

• E and B are in phase

• Accelerating electric charges produce electromagnetic waves

v = 1

√

= 8.85 X 10-12 C2/Nm2 (permittivity)

X 10-7 Ns2/C2 (permeability)

Calculate the speed of light using these constants

Speed of EM Waves

Wave Properties

• First man-made EM waves detected by Hertz (8 years of Maxwell’s death)

= wavelength (meters)

f = frequency (cycles/s or Hertz)

f = c

(in a vacuum)

Electromagnetic Spectrum

• Visible light

• 4 X 10-7 m to 7X 10-7 m (400 to 700 nm)

• Electrons– Radio – running electrons up and down an antenna– Electrons moving within atoms and molecules– X-rays - Electrons are rapidly decellerated by striking

metal

• Gamma Rays – Nuclear decay

Waves: Ex 1

Calculate the wavelength of a 60 Hz EM wave

f = c = c/f = (3.0 X 108 m/s)/60 s-1 = 5 X 106 m

What range of the spectrum is this?

Waves: Ex 2

Calculate the wavelength of a 93.3 MHz FM radio station

f = c = c/f = (3.0 X 108 m/s)/(93.3 X 106 s-1) = 3.22 m

Waves: Ex 3

Calculate the frequency of 500 nm blue light.

f = c

f= c/f = (3.0 X 108 m/s)/500 X 10-9 m = 6 X 1014 Hz

Waves: Ex 4

When you speak to a telephone to someone 4000 km away, how long does it take the sound to travel?

v = d/t

t = d/v

T = (4000 X 103 m)/(3 X 108 m/s) = 1.3 X10-2 s

Speed is less because of wires

Measuring the Speed of Light

• Galileo – Tried to measure from mountaintop to mountaintop.

• Roemer – Measured time needed for light to travel from Io (Jupiter’s moon)

• Michealson’s Experiment

• Measured time needed for light to travel and be observed

• Only certain rotational speeds allowed observer to see the light

• Tried it on mountains in southern California (35 km)

c = 2.99792458 X 108 m/s

c = 3.0 X 108 m/s

• Slightly slower in air

• Same for all EM waves

Energy and EM Waves

• All EM waves carry energy

• Exactly half by electric field and half by magnetic field

E = cB (relates E and B)

S = ½ ocE2o = ½ cB2

o

o

(ave rate of energy transported per unit area, per unit time)

Radio Transmitter

• Carrier Frequency – Frequency that one “tunes in”

• AM - 530 to 1600 kHz

• FM – 88 to 108 MHz

• Broadcast TV - 54 to 88 mHz, 174 to 216 MHz

AM Radio

• Amplitude Modulated

• Program signal mixes with carrier signal

• Frequency of wave does not change, only amlitude

FM Radio

• Frequency Modulated

• Frequency of total signal varies (slightly)

• 101.3 and 101.5 but never 101.4

Receiving a Signal

• Straight Antenna – Electric field of EM wave produces a current in the electrons in the antenna

• Loop Antenna – Magnetic field of EM wave induces a current

• Tune in a station – uses the resonant frequency of an LC circuit (variable capacitors/inductors)

Radio: Ex 1

An FM station is 103.1 mHz. Calculate the wavelength:

f = c = c/f = (3.0 X 108 m/s)/(103.1 X 106 s-1) = 2.91 m

What is the value of the capacitance for this tuning circuit if L = 0.40 H?

fo = 1

2 √LC

C = 1/(42fo2L)

C = 1/ (4)(3.14)2(1.0x108