When we say current, I, through a wire is uniform, what do we mean?

[pardesi]

when we say the current through a wire is uniform and is I what do we mean

 

[chroot]

Consider the circular cross-section of the wire. Now consider just the top half-circle, and the bottom half-circle.

If the current is uniformly distributed through the wire, then the current through each of these half-circles is the same: I/2.

Generally, if the current is uniformly distributed through the wire, the any two regions of the cross-section with the same area will be carrying the same current.

- Warren

 

[pardesi]

and does the current is i mean the current through the cross section perpendicular to current flow

 

[chroot]

Usually, yes.

- Warren

 

[pardesi]

ok two more.
how do u define surface current density
also when we say in cas eof steady current the current through the wire is i what do we mean

 

[olgranpappy]

The answers to the question of definition can be found in any textbook. I would suggest that you look in the appendix of Griffith's--maybe under "surface current" or "current, surface"?

 

[pardesi]

The answers to the question of definition can be found in any textbook. I would suggest that you look in the appendix of Griffith's--maybe under "surface current" or "current, surface"?

i am asking u after reading from griffith

 

[jtbell]

How does Griffith define surface current density and what, specifically, don't you understand about that definition?

 

[pardesi]

well he says and i quote

consider a "ribbon" of infitesmal width dl_{p} running parallel to current flow and let the current through this be dI then we define surface current density K as K=\frac{dI}{dl_{p}} where dl_{p} is taken perpendicular to current flow

well what i don't understand about this is why should we take a 'ribbon' isn't a small width enough to define .also if a take a width then the current flowing across it in general would depend on the ribbon length

 

[Meir Achuz]

well what i don't understand about this is why should we take a 'ribbon' isn't a small width enough to define .also if a take a width then the current flowing across it in general would depend on the ribbon length

Surface current denslity is current per unit width of Griffith's ribbon, so
K times the width is the current.

 

[Meir Achuz]

A somewhat more mathematical definition of surface current density is
"The surface current density is defined so that the current flowing past a differential line element
{\vec dL} on the surface is given by
<br /> dI={\vec K}\cdot({\vec dL}\times{\vec n}),
where {\vec n} is a unit vector normal to the surface."

 

[pardesi]

but since the ribbon has length and we have taken it along the flow of current won't the current depend on length of ribbon

 

[olgranpappy]

well he says and i quote


well what i don't understand about this is why should we take a 'ribbon' isn't a small width enough to define .also if a take a width then the current flowing across it in general would depend on the ribbon length

The ribbon is introduced for visualization purposes. the surface current density is a local property and doesn't depend on any "ribbon" or "ribbon length" introduced as a pedogogical aid.

The surface currect density is a vector in the plane of the surface and in the direction of the current flow at a point. It's magnitude is proportional to the strength of the current I at the point.

If you integrate the surface current density along some line \vec \ell(s) embedded in the surface (here my line is parametrized by the real number s) you get the current flowing across that line:
<br /> I_{\textrm{across line}}=\int d|\ell|\hat t\cdot \vec K<br />
where \hat t is the one of the two unit vectors perpendicular to \frac{d\vec \ell}{ds} whose angle with \vec K is smallest.