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

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

Faraday’s law in differential form

Ampere’s law in differential form

Maxwell’s eqns for postulated EM wave

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?

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

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

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

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

Maxwell equations  Light

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 =