- #1
Wminus
- 173
- 29
For a good conductor, an incoming plane electromagnetic wave will be attenuated exponentially as it penetrates a distance ##z## into the conductor, ##|\vec{E}(z)| = |\vec{E_0}|e^{-z/ \delta}##. ##\delta## is called the "skin depth". The current generated by this incoming electromagnetic wave is given by ohm's law and thus will be attenuated in the same fashion ##\vec{J_E} = \sigma \vec{E} \Rightarrow |\vec{J_E(z)}| = |\vec{J_{E0}}|e^{-z/ \delta}##.
OK, this is all fair enough. It falls out from maxwell's equations.
However, if you have a cylindrical conductor and you connect it to a high-frequency AC power source, it turns out that that the resulting electrical current ##\vec{J_{AC}}## will have the exact same distribution as ## \vec{J_E}##. Namely, ##\vec{J_{AC}} = \vec{J_{AC0}} e^{-z/ \delta}##, with the exactly same attenuation factor (delta) as before.
Why is this so? Does this mean an AC power source generates a potential difference in the conductor in the same way an incoming electromagnetic wave does?
OK, this is all fair enough. It falls out from maxwell's equations.
However, if you have a cylindrical conductor and you connect it to a high-frequency AC power source, it turns out that that the resulting electrical current ##\vec{J_{AC}}## will have the exact same distribution as ## \vec{J_E}##. Namely, ##\vec{J_{AC}} = \vec{J_{AC0}} e^{-z/ \delta}##, with the exactly same attenuation factor (delta) as before.
Why is this so? Does this mean an AC power source generates a potential difference in the conductor in the same way an incoming electromagnetic wave does?