1. Electromagnetism Giancoli Ch.21-29 Physics of Astronomy, winter week 7
Review of waves and wave equations
Summary of EM & Maxwell’s eqns
Derive EM wave equation and speed of light!
Magnetic monopole  more symmetry
Today: to American Physical Society meeting!
Next Friday 1:00-2:00 in 1050 Lab I: Science Carnival poster session

2. Waves

3. Wave equation 1. Differentiate dD/dt  d2D/dt2
2. Differentiate dD/dx  d2D/dx2
3. Find the speed from

4. Causes and effects of E Gauss: E fields diverge from charges
Lorentz force: E fields can move charges
F = q E

5. Causes and effects of B Ampere: B fields curl around currents
Lorentz force: B fields can bend moving charges
F = q v x B = IL x B

6. Changing fields create new fields!
Faraday: Changing magnetic flux induces circulating electric field
Guess what a changing E field induces?

7. Changing E field creates B field!
Current piles charge onto capacitor
Magnetic field doesn’t stop
Changing electric flux
“displacement current”
magnetic circulation

8. Partial Maxwell’s equations

9. 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 Ampere’s laws?

10. Faraday + Ampere

11. Sub in: E=E0 sin (kx-wt) and B=B0 sin (kx-wt)

12. Speed of Maxwellian waves?
Faraday: -wB0 = k E Ampere: m0e0wE0=kB0
Eliminate B0/E0 and solve for v=w/k
e0 = 8.85 x C2 N/m2
m0 = 4 p x 10-7 Tm/A

13. Maxwell equations  Light
E(x,t)=E0 sin (kx-wt) and B(x,t)=B0 sin (kx-wt)
solve Faraday’s and Ampere’s laws.
Electromagnetic waves in vacuum have speed c and energy/volume = 1/2 e0 E2 = B2 /(2m0 )

14. Full Maxwell equations
Notice the asymmetries – how can we make these symmetric by adding a magnetic monopole?