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Maxwell’s equations • Wave equations • Plane Waves

Massachusetts Institute of Technology RF Cavity and Components for Accelerators 1 Massachusetts Institute of Technology RF Cavity and Components for Accelerators USPAS 2010 Maxwell s equations Wave equations Plane Waves Boundary conditionsA. Nassiri -ANLL ecture1-ReviewMassachusetts Institute of Technology RF Cavity and Components for Accelerators 2 Maxwell s EquationsThe general form of the time-varying Maxwell s equations can be written in differential form as:0= = = += BDBEDJH ttMassachusetts Institute of Technology RF Cavity and Components for Accelerators 3A few other fundamental relationshipsH/m104 F/m,108548with ity)(permeabil and ity)(permittiv hereips"relationsh veconstituti" equation" continuity" law" sOhm'" 7012000 = === == = =.

The solution represents a wave travelling in the +z direction with velocity c. Similarly, f(z+vt) is a solution as well. This latter solution represents a wave travelling in the -z direction. So generally, E x (z,t)= f [(x±vt)(y ±vt)(z ±vt)] In practice, we solve for either E or H and then obtain the. other field using the appropriate curl ...

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