Flux of the Poynting vector

[enerieire]

I have some problems in calculating the flux of Poynting's vector through a surface.
I have that:

S=c/4π⋅H^2⋅n (S: Poynting's vector, n: versor of the direction of the propagation of the em wave)

H=1/cR A'
but: A=(1/cR) d'; A'=(1/cR) d'' ==> H= (1/cR)^2 d''
==> S= (c/4π)⋅ 1/(cR)^4 d''^2 nI have to find that the result of the flux of S (I don't know through which surface) is:

dE/dt=∫S⋅dΩ=...=-2/(3⋅c^3) |d''|^2 (d is magnetic dipole momentum)

How is it calculated?
Thanks to everyone who will try to help me.

 

[mark726]

Hello,

To calculate the flux of Poynting's vector through a surface, you will need to use the formula dE/dt = ∫S⋅dΩ, where dE/dt is the time derivative of the electric field, S is Poynting's vector, and dΩ is the surface element.

First, you will need to determine the direction of the electric field, which is given by the versor n. This will give you the direction in which the electromagnetic wave is propagating.

Next, you will need to calculate the magnitude of Poynting's vector using the formula S=c/4π⋅H^2⋅n, where c is the speed of light, H is the magnetic field, and n is the direction of propagation.

To calculate the magnetic field H, you will need to use the formula H=1/cR A', where R is the distance from the source of the electromagnetic wave, and A' is the magnetic vector potential.

The magnetic vector potential A' can be calculated using the formula A'=(1/cR) d', where d' is the magnetic dipole moment. Substituting this into the formula for H, we get H=(1/cR)^2 d''.

Now, substituting this value of H into the formula for Poynting's vector, we get S= (c/4π)⋅ 1/(cR)^4 d''^2 n.

Finally, to find the flux of Poynting's vector through a surface, we will integrate S over the surface element dΩ. This will give us the total energy flux through the surface.

The final result for the flux of Poynting's vector will be dE/dt=∫S⋅dΩ=...=-2/(3⋅c^3) |d''|^2. This is the result you were given in the forum post.

I hope this explanation helps you understand how to calculate the flux of Poynting's vector through a surface. If you have any further questions, please let me know.