Electromagnetism and Energy

1
Electromagnetism and Energy

• Causes and effects of
• static and dynamic
• electric magnetic fields
• Maxwell equations yield
• electromagnetic waves
• Electromagnetic energy

• Thermal energy
• heating, melting, boiling,
• Potential energy
• electrostatic, gravitational
• Kinetic energy
• Bernoulli equation

2
ElectrodynamicsGiancoli Ch.21-29Physics of
Astronomy, winter week 6

• Star Date
• HW finish CO 3.6, magnitudes
• Overview of EM Maxwells eqns
• Minilectures
• Derive EM wave equation and c
• Next week write Interim Research Planning
  Report
• Boas Ch.4 partial differentiation (1-6)
• Week 8 Modern physics CO Ch.5 Interaction
  of light and matter

3
Causes and effects of E

• Gauss E fields diverge from charges

• Lorentz E fields can move charges
• F q E

4
Causes and effects of B

• Ampere B fields curl around currents

• Lorentz B fields can bend moving charges
• F q v x X IL x B

5
Changing fields create new fields!

• Faraday Changing magnetic flux induces
  circulating electric field
• Guess what a changing E field induces?

6
Changing E field creates B field!

• Current piles charge onto capacitor
• Magnetic field doesnt stop
• Changing
• ? displacement current

7
Maxwells equations
8
Maxwell eqns ? electromagnetic waves

• Consider waves traveling in the x direction with
  frequency f w/2p
• and wavelength l 2p/k
• E(x,t)E0 sin (kx-wt) and
• B(x,t)B0 sin (kx-wt)
• Do these solve Faraday and Amperes laws?

9
Faraday Ampere
10
Sub in EE0 sin (kx-wt) and BB0 sin (kx-wt)
11
Speed of Maxwellian waves?

• Ampere
• B0/E0 m0 e0 v

• Faraday
• B0/E0 1/v

Eliminate B0/E0 and solve for v
e0 8.85 x 10-12 C2 N/m2
m0 4 p x 10-7 Tm/A
12
Maxwell equations ? Light
E(x,t)E0 sin (kx-wt) and B(x,t)B0 sin
(kx-wt) solve Faradays and Amperes
laws. Electromagnetic waves in vacuum have speed
c and energy/volume 1/2 e0 E2 B2 /(2m0 )