Power Loss Of An EM Wave Hitting A Cu Wire

[H_man]

Hi all, :uhh:

I am trying to calculate the loss in power of a wave which is partially

reflected and partially transmitted from a wire.


The skin depth of the wire is many times the thickness of the wire.

My first attempt to solve this problem was to consider seperately the

energy lost due to currents induced by the electric field and then the

magnetic field.


I started by calculating the skin depth of the Cu wire in order to

calculate the effective resistance at the frequency of the wave.

I then thought to calculate the current I, by first taking J₀=sigma.E,

using the electric field derived from the Poynting vector and the

conductivity of Cu. Then integrating with respect to area bearing in

mind that J falls off exponentially from the surface.


Finally to use P=I²R to determine power loss from the electric field.

The answer I got was non-sensical.


When then trying to calculate the losses from the changing magnetic

field I found the helpful expression:
I/l = H (where I is the current, l the length of the field in the

conductor and H the field strength).


The book didn't show any calculation relating to the electric field

which makes me think I've been barking up the wrong tree and in fact the

only losses which occur are entirely due to the magnetic field. However,

I find this very very confusing, why should one field do work and not

the other?

I think I am possibly missing some basic physical knowledge

 

[mark726]

here.



Hi there,

Calculating the loss in power of a wave that is partially reflected and transmitted from a wire is indeed a complex problem. However, your approach of considering the electric and magnetic fields separately is a good starting point.

Firstly, it is important to note that both the electric and magnetic fields contribute to the power loss in a wave. The electric field induces currents in the wire, which then dissipate energy as heat due to the resistance of the wire. On the other hand, the changing magnetic field also induces currents in the wire, leading to the same dissipation of energy as heat.

In your approach, you correctly calculated the skin depth of the wire to determine the effective resistance at the frequency of the wave. However, when calculating the current using J0=sigma.E, it is important to consider the direction of the electric field and the orientation of the wire. This will affect the direction and magnitude of the induced current, which in turn affects the power loss.

Similarly, when calculating the losses from the changing magnetic field, it is important to consider the orientation of the wire with respect to the magnetic field. The expression I/l = H is a good starting point, but it may need to be modified depending on the geometry of the wire and the direction of the magnetic field.

In summary, both the electric and magnetic fields contribute to the power loss in a wave that is partially reflected and transmitted from a wire. It is important to consider the direction and orientation of both fields when calculating the power loss. I hope this helps in your calculations. Good luck!