How is converted the energy of a E.M. wave in a conductor

[happyparticle]

Homework Statement

How is converted the energy of a E.M. wave in a conductor

Relevant Equations

$u_i = u_e + u_m$

I'm thinking about how the energy is conserved when a E.M. wave pass through a conductor.
If a E.M. pass through a conductor, the electrons must move "oscillated", thus the energy from the E.M. wave is converted to kinematic energy.
Another way I see that is the E.M wave must generate a current.
I don't know if my intuition is correct, but either way, I can't prove the conservation of energy. The initial energy $u_i = u_e + u_m \neq u_f + \frac{1}{2}mv^2$
I must forget something or it's not as simple as that.

 

[tech99]

The electric field of the wave creates a voltage along the wire. This then creates a current in the wire dictated by the resistances and reactances which are present. (Notice that a piece of wire has its own distributed L and C even without adding anything to make a circuit). When the current flows, it means that electrons have been accelerated, and when they do this they radiate. For a wire having no resistance, any energy which is intercepted will be re-radiated due to electron acceleration. For a wire in a circuit with resistance, some of the energy intercepted will be re-radiated, the remainder warming the resistor.
The electrons have very small mass, so KE is negligible, but when they move they create a magnetic field, and this stores energy as if it were a mass. This gives inertia, as if we had mass.
The inertia means that the acceleration of the electrons in response to an incoming wave may be delayed, in a similar way to current in an inductor. Phase shift also arises due to capacitance in the circuit. The re-radiated wave will combine with the incoming wave causing it to be weaker due to the intercepted energy. However, if the re-radiated energy is shifted in phase, the passing EM wave can exhibit effects such as a shadow, or a bright reflection.
Notice that the physical length, shape and components of the circuit will, in a complex way, influence the power which is intercepted.