# Current through the conductor

DODGEVIPER13

## Homework Statement

The current density in a cylindrical conductor of radius a placed along the z-axis is J=10e^-(1-ρ/a)Uz
Find the current through the cross-section of the conductor.

I=JA
A=(pi)a^2

## The Attempt at a Solution

So far I have this I=10e^-(1-ρ/a)Uz((pi)a^2) which I assume I am to integrate but what should I integrate with respect too and what should the limits be I am guessing from 0 to a?

Gold Member
You integrate the flow normal to the cross section through which it is flowing.

DODGEVIPER13
So that would be along the x or y?

DODGEVIPER13
The normal is the perpendicular vector right?

Gold Member
Yes, the normal is perpendicular to the surface.

DODGEVIPER13
ok so a normal vector equals to Uz/Uz (where the bottom Uz is the length of Uz it is in between those two absolute value mark things). Do you have any more hints on how to set this up