From Griffiths' Intro to electrodynamics:
Now I'm confused about 3 things:
1) What is the 'mobile' surface charge density? Isn't the surface current density itself the 'mobile' surface charge density?
2) Is the small current $dI$ in the whole ribbon or only part of the ribbon? I'm guessing its the whole ribbon of width $dl$ but I want to make sure.
3) If I'm asked to find the surface current density as follows:
Is the current flowing only on the surface of the wire or is it flowing naturally through the whole volume of the wire and I need to only account for the current on the surface? , I'm able to derive $K$ will be equal to $I/2\pi a$ mathematically, but if the current is flowing throughout the volume of the wire, how can I visualize the unit length perpendicular to that flow? Thanks I hope I was clear about the questions
Best Answer
Not all charges are mobile. For instance, protons and most electrons in a solid metal are not mobile. So, here, surface charge density could be interpreted as a surface density of free electrons.
Yes, dl is the width of the whole ribbon.
The current density is not always uniformly distributed through the whole volume of a conductor: most of a high frequency AC current, due to the skin effect, flows in a thin layer under the surface of a conductor. In such cases, it makes sense to talk about a surface current or a surface current density.
As mentioned earlier, the current can flow mostly along the surface of a wire, in which case, the conventional current density, a current through a unit area of the wire's cross-section, could be replaced by the surface current density, a current through a unit length of the wire's circumference.