Physics challenge

lagrangian1125 SG

Using 4 maxwell eqns on electrodynamics
see
http://en.wikipedia.org/wiki/Maxwell%27s_equations

Derive the speed of any electromagnetic wave.

eagle SG

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 SG

Seems not much reply Crying or Very sad .
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 SG

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 SG

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