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 Maxwell Maxwell’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 E 2 or B 2

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 C 2 /Nm 2 (permittivity)    X Ns 2 /C 2 (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 m to 7X 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 10 8 m/s)/60 s -1 = 5 X 10 6 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 10 8 m/s)/(93.3 X 10 6 s -1 ) = 3.22 m

Waves: Ex 3 Calculate the frequency of 500 nm blue light. f  = c f  = c/  f = (3.0 X 10 8 m/s)/500 X m = 6 X 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 10 3 m)/(3 X 10 8 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 = X 10 8 m/s c = 3.0 X 10 8 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  o cE 2 o = ½ cB 2 o  o (ave rate of energy transported per unit area, per unit time)

Radio Transmitter Carrier Frequency – Frequency that one “tunes in” AM 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) and 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 mHz. Calculate the wavelength: f  = c = c/f = (3.0 X 10 8 m/s)/(103.1 X 10 6 s -1 ) = 2.91 m

What is the value of the capacitance for this tuning circuit if L = 0.40  H? f o = 1 2  √LC C = 1/(4  2 f o 2 L) C = 1/ (4)(3.14)2(1.0x108