# Finding expression for non-uniform current density of a wire

1. Nov 20, 2015

### phys-student

1. The problem statement, all variables and given/known data
A long, straight wire, radius R, carries total current I. The current is distributed in the wire so that the current
density is proportional to s, the distance from the center of the wire.
(a) Write an expression for the current density J in the wire, as a function of s.

2. Relevant equations
J=dI/da

3. The attempt at a solution
J=2*s*I/R2
I'm pretty sure my attempted solution is correct because when you integrate J from 0 to R with respect to s you get the total current I. However I kinda just pulled this out of thin air and I'm pretty sure I won't get full marks without showing my work. Is there a different way to do this besides just making up an expression for J like I did?

2. Nov 20, 2015

### TSny

How would you express this statement in mathematical form?

3. Nov 20, 2015

### phys-student

I don't know, that's what I'm trying to understand. I was trying to express that statement in mathematical form but couldn't figure it out, so I settled on the expression that I have simply because integrating it over the cross section of the wire results in the total current I

4. Nov 20, 2015

### SammyS

Staff Emeritus
I'm pretty sure that's not right. Even the units are wrong.

Likely you're not integrating over an area.

5. Nov 20, 2015

### phys-student

Yep you're right. Totally forgot that I also need to integrate over the angle from 0 to 2 pi

6. Nov 20, 2015

### phys-student

Okay I'm good now, thanks