Physics challenge

• lagrangian1125

  14 Aug 07, 18:14

  Using 4 maxwell eqns on electrodynamics
  see
  http://en.wikipedia.org/wiki/Maxwell%27s_equations
  
  Derive the speed of any electromagnetic wave.
  
• eagle

  14 Aug 07, 23:31

  Read before in Resnick and Halliday textbook with a simplified method, but forgot how.
  
  But the following site may help you:
  
  http://www.phy.davidson.edu/StuHome/cabell_f/coaxial/pages/Speedd.html
  This method involves lots of vector calculus. But you must understand what is a curl and what is a divergence.
• lagrangian1125

  15 Aug 07, 01:59

  Seems not much reply .
  Ok the sketch is find laplacian of E field and B field. Since Laplacian of an arbitrary function is equal to (1/v^2)(2nd order partial diff of the function)
  
  We can immediately equate the speed of EM waves to be 1/(permitivity times permeablility of free space)^0.5 which is equals to c, the speed of light.
• eagle

  15 Aug 07, 21:02

  hmmm...
  
  I don't really understand this part
  

  Since Laplacian of an arbitrary function is equal to (1/v^2)(2nd order partial diff of the function)

  Can explain more? Thanks
• lagrangian1125

  16 Aug 07, 15:04

  Originally posted by eagle:

  hmmm...
  
  I don't really understand this part
  
  Can explain more? Thanks

  Rather let f be an arbitary funct that rep displacement of a particular point in a wave.
  f=f(x,t)
  
  Using newton 2nd law, and chain rule for partial derivative, u get
  d2f/dz2=(1/v^2)(d2f/dt2)
  
  Where it should actually be partial derivative.( just that I cant find the right symbol.)
  
  Comparing with laplacian of B field and E field, u realize they actually share the same constants, together with above result, equate the constant=(1/v^2) as they are all in the same mathematical form, you get the result.
  
  c=1/(permittivity* permeability of free space)^0.5