maxwell's equations in the frequency domain
alex
Firstly I susbstituted the fourier decomposition of an electric field
into the vector maxwell equation rot E(r,t) = mo part d/dt H (r,t)
E(r,t) = 1/2pi integral E(r,w)e^wt dw
LHS Took the cross product inside the integral
RHS took the time derivative inside the integral
Then consider how to take the time deriv of the H (r,w), which is a
complex vector in the frequency domain.
Use the defintion of fourier transform to then rewrite H in time
domain to perform partial deriv wrt time
Inside the integral is then a partial derivative of a product.
part d/dt (E(r,t)e^iwt) = E(r,t). iwe^iwt + e^iwt. partial d/ dt E
(r,t)
Using that rule I get term cacnelling to zero.
What's wrong
I am sorry its difficult to understand, but don't have acces to a
scanner to post my working out.
Any help greatfully recieved...
Thanks
ALex
Timo Nieminen
> Hope someone can help.. I just can't see where I have gone wrong.
>
> Firstly I susbstituted the fourier decomposition of an electric field
> into the vector maxwell equation rot E(r,t) = mo part d/dt H (r,t)
>
> E(r,t) = 1/2pi integral E(r,w)e^wt dw
>
> LHS Took the cross product inside the integral
> RHS took the time derivative inside the integral
>
> Then consider how to take the time deriv of the H (r,w), which is a
> complex vector in the frequency domain.
>
> Use the defintion of fourier transform to then rewrite H in time
> domain to perform partial deriv wrt time
>
> Inside the integral is then a partial derivative of a product.
>
> part d/dt (E(r,t)e^iwt) = E(r,t). iwe^iwt + e^iwt. partial d/ dt E
> (r,t)
>
> Using that rule I get term cacnelling to zero.
>
> What's wrong
For a Fourier component E(r)*exp(iwt), the E(r) is not a function of time.
E(r) is the time-independent amplitude (density) of the Fourier component
of angular frequency w.
Presumably, you mean H, since the time derivative is of H, not E, but the
same point holds.
--
Timo