What is the relationship between AC electricity and transverse waves in copper?

[HWGXX7]

I was wondering if I may interprete AC current as a tranverse wave trough copper as medium. So this wave behaviour has a general wave-form written as: $$\zeta(x,t)=\zeta_{0}sin(kx-\omega.t)$$
This is a solution to the partial differential equation:
$$\frac{\partial^{2}\zeta}{\partial t^{2}}=K.\frac{\partial^{2}\zeta}{\partial x^{2}}$$

K is the medium-depent factor, which will determine the wave velocity.
Because the electric!ty will only be a one direction flow (assume we talk about a period in 50Hz current), the derivative to x direction wille be meaningless..I think.

But electricity is the flow of electrons, so the medium itself will be responsible for the wave. This bothers my whole perception of the above approach...

Anyway who shares same ideas?

grtz

 

[Bob S]

The complete wave equation for any electromagnetic wave component φ is
$$\frac{\partial^2\psi}{\partial t^2 }=\frac{1}{\varepsilon \mu} \frac{\partial^2 \psi}{\partial x^2}- \frac{\sigma}{\varepsilon}\frac{\partial \psi}{\partial t }$$
where ε and μ are the permittivity and permeability, and σ is the conductivity of the medium. In free space, the speed of light is c = 1/√ (εμ).

The general solution of the above wave equation is of the form
$$\psi \left( x,t \right)=\psi_o e^{-ax}e^{i \left( \omega t - bx \right)}$$
where the e^-ax factor represents attenuation and e^i(ωt-bx) represents propagation.

If power (electromagnetic wave) is traveling along two parallel wires, the power may be represented by two orthogonal fields (E and H) traveling between the wires (look up Poynting vector), and there are no E fields in the wires, unless the wires have resistance. A longitudinal current I in the wire is orthogonal to the magnetic field H between the wires.

Bob S

 

[HWGXX7]

Thank for the reply, so in general the approach to see electricty (AC) as a wave through material is correct.

The use of H instead of B is because H is the magnetic field and B is just magnetic induction, correct?

In extend, I also assume the whole world is than build up from only (a)periodic waves.

I find it very interesting that maybay it is possible to determine all behaviour from just wave behaviour, instead of analysing structures.

Could it be possible for example to analyse the disfunction of a structure just by de sound wave it produces?

Sorry if I go beyond my question, just wondering.

grtz

 

[MisterX]

Thank for the reply, so in general the approach to see electricty (AC) as a wave through material is correct.

The use of H instead of B is because H is the magnetic field and B is just magnetic induction, correct?

$\mathbf{H}\ \equiv \ \frac{\mathbf{B}}{\mu_0}-\mathbf{M}$ (from Wikipedia)

and thus
$B = \mu_0(H + M)$

The B field is thought of as sum of the magnetic field due to the magnetization of the material (M) and the H field.

 

[HWGXX7]

Well, but B isn't the field itself? The gradient of amps.winding is H. This has the characteristic of a field. B is magnetic induction and equals permeability.H

H is the concept of magnetic field, but de induction B which occurs, depents on which material is being magnetised.