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

1. Aug 7, 2007

### pardesi

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

Last edited: Aug 7, 2007
2. Aug 7, 2007

### chroot

Staff Emeritus
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

3. Aug 7, 2007

### pardesi

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

4. Aug 7, 2007

### chroot

Staff Emeritus
Usually, yes.

- Warren

5. Aug 7, 2007

### 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

6. Aug 7, 2007

### 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"?

7. Aug 8, 2007

8. Aug 8, 2007

### Staff: Mentor

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

Last edited: Aug 8, 2007
9. Aug 8, 2007

### pardesi

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

10. Aug 8, 2007

### Meir Achuz

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

11. Aug 8, 2007

### 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
$$dI={\vec K}\cdot({\vec dL}\times{\vec n})$$,
where $${\vec n}$$ is a unit vector normal to the surface."

12. Aug 8, 2007

### 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

13. Aug 8, 2007

### olgranpappy

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:
$$I_{\textrm{across line}}=\int d|\ell|\hat t\cdot \vec K$$
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.