1. Winter wk 9 – Mon.28.Feb.05 Energy Systems, EJZ

2. Maxwell Equations in vacuum Faraday: Electric fields circulate around changing B fields Ampere: Magnetic fields circulate around changing E fields

3. Faraday’s law in differential form

4. Ampere’s law in differential form

5. Maxwell’s eqns for postulated EM wave

6. Do wave solutions fit these equations? Consider waves traveling in the x direction with frequency f=   and wavelength =  /k E(x,t)=E 0 sin (kx-  t) and B(x,t)=B 0 sin (kx-  t) Do these solve Faraday and Ampere’s laws? Under what condition?

7. Differentiate E and B for Faraday Sub in: E=E 0 sin (kx-  t) and B=B 0 sin (kx-  t)

8. Differentiate E and B for Ampere Sub in: E=E 0 sin (kx-  t) and B=B 0 sin (kx-  t)

9. Maxwell’s eqns in algebraic form Subbed in E=E 0 sin (kx-  t) and B=B 0 sin (kx-  t) Recall that speed v =  /k. Solve each equation for B 0 /E 0

10. Speed of Maxwellian waves? Ampere B 0 /E 0 =  0   v Faraday B 0 /E 0 = 1/v Eliminate B 0 /E 0 and solve for v:  0  =  x    m    =  x    C 2 N/m 2

11. Maxwell equations  Light

12. Energy of EM waves Electromagnetic waves in vacuum have speed c and energy/volume = E and B vectors point (are polarized) perpendicular to the direction the wave travels. EM energy travels in the direction of the EM wave. Poynting vector =