Uniformly Distributed Current in a Wire: Question Explained

[leelee]

ive posted this in the other forum, but haven't received a reply, so trying again :)

Question:
-straight wire with radius R, carrying current I
-current is uniformly distributed across the cross sectional area of wire
-calculate the magnetic field inside wire as function of distance r from the center of the wire

In the solution, there is a picture of the cross section of the wire, and the current is going into the page, ie X.
there is an imaginary circle, "amperian loop" with radius r, inside the wire.
then, B*2*pi*r = u*i_inside (equation 1)
then i_inside = I*(pi*r^2)/(pi*R^2) = I*r^2/R^2 (equation 2)
This i don't understand. I know it something to do with the fact that current is uniformly distibuted, but how to get equation 2?
Is it just a ratio?
Thanks!

 

[siddharth]

It's given that current is uniformly distributed across the cross section of the wire. So, if you want to find the current density(current per unit cross sectional area), it will be $$\frac{I}{A}$$ which is $$\frac{I}{\pi R^2}$$.
From this current density, how will you find the current inside a cross-sectional area with radius 'r'. Can you see how equation 2 follows?

 

[leelee]

Ah, yes i understand now. Thanks Siddharth!