Electromagnetic Waves

Maxwell’s Equations

  • Maxwell’s Equations 

E



B

  

d A



d A

   0

Q

0  

E



B

  

d s



d s

     0

I d



m dt

  0  0

d



e dt

• Lorentz Force 

F

 

q E



q v

  

B

Displacement Current

• Flowing current generates a magnetic field, but what about inside a capacitor where current doesn’t flow?

I • A changing electric field also generates a magnetic field.

 

B



d s

   0  0

d



dt e

E

I

B

Wave Propagation in 3-D

• Plane Waves - Crests of the 3 dimensional wave lie in a plane. Intensity remains constant.

• Faraday’s Law 

E



x



B



x

  • Ampere’s Law    

B



t

0 0 

E



t

Solution is

E B



k

  

E m B m



f

cos cos 

c

 

kx



kx

  

t



t

  1  0  0

Properties of EM Waves

• E & B fields satisfy the same wave equation.

• EM waves travel at velocity,

c

 1  0  0 • E & B fields are perpendicular to each other and to the direction of travel.

• Magnitude of E & B fields obey

c



E B

• EM waves obey the superposition principle.

Polarization

• Preferential orientation of the wave’s electric field vectors.

Electric Wave Magnetic Wave

v

Randomly Oriented Light Vertically Polarized Light

I



I

0 cos 2 

EM Spectrum

Decreasing Wavelength  

f



c

Increasing Frequency – Radio waves – Microwaves – Infrared Light (IR) – Visible Light – Ultraviolet Light (UV) – X-Rays – Gamma Rays Speed - 3.0 × 10 8 m/s

Energy in an EM Wave

• Poynting vector - Rate at which energy flows through a unit surface perpendicular to the flow. (Units, W/m 2 )

S

   1 0 

E

 

B

Electric Wave • Wave Intensity Magnetic Wave

v I



S



E

2

m



B m

0

Radiation Pressure

• Light has no mass; however, it does have momentum.

• For complete absorption of light (inelastic collision), the pressure is

P



I c

• For complete reflection of light (elastic collision), the pressure is

P

 2

I c

Doppler Shift

• For sound waves • For light

f

' 

f

 

v v

 

v o v s

  Remember:  

f

– Light has no medium of propagation – +v is motion towards the observer 

c f

' 

f c



v c



v

Star Spectra Sloan Digital Sky Survey

Evidences for IBB

• Hubble Constant • Nucleosynthesis – 73% H, 24% He, 3% other • Microwave Background • Large Scale Structure • Evidence of Dark Matter

• How does distant light get to us?

– Light created in transit.

– Speed of light is slowing down.

– White hole cosmology – Non-uniform properties of space

Young Creation Models

Big Bang Critique

• Quintessence • Exotic Dark Matter • Laws of Thermodynamics • Inflation – Exceed speed of light by 10 24 × • Not constrained enough – “...supporters of Big Bang cosmology gain for themselves a large bag of free parameters that can subsequently be tuned as the occasion may require.” (Burbidge, Hoyle, & Narlikar)

Composition of the Universe: 4% atoms, 23% cold dark matter, 73% dark energy

Kepler Mission

• Description – Launched March 2009 – View 145,000 stars near Cygnus – Observe planet transits – Stabilization failed May 2013 • Results as of Nov. 2013 – 3538 candidate planets – 10 earth sized in habitable zone – Nearest maybe 12 light years away