Maxwell

1
Maxwells Equations

• By Scott Riggs

2
Divergence and Curl

• Divergence (scalar)
• ? A dAx/dx dAy/dy dAz/dz
• Measure of how much A spreads out from the point
  in question
• Curl (vector)
• ? x A (dAz/dy - dAy/dz)i (dAx/dz - dAz/dx)j
  (dAy/dx dAx/dy)k
• How much A curls around the point in question.
  (How rotational A is).

3
Gausss Law

• ? E 4p? (? is the charge density)

4
No MM Law

• ? B 0

5
Faradays Law

• ? x E -(1/c)(dB/dt)

6
Amperes Law

• ? x B (1/c)(dE/dt) (4p)J
• J is the volume current density

7
Maxwells Equations

• With ? and J 0
• ? E 0
• ? B 0
• ? x E (1/c)(dB/dt) 0
• ? x B - (1/c)(dE/dt) 0
• // plate capacitor
• Changing E induces a changing B and can have a
  wave that lives forever

8
Electromagnetic waves in a Vacuum

• Take the curl of ? x (? x E) (1/c)(d/dt)(? x B)
  0
• ?(?E) -?2E (1/c)(d/dt)(1/c)(dE/dt) 0
• -?2E (1/c2)(d2E/dt2) 0
• Equation for a wave
• Can do the same thing for the magnetic field
• Propogation of Electromagnetic Wave