The question is: How can I find the magnetic field inside a long conductor?

[humanist rho]

Homework Statement

I have to find the magnetic field inside a long conductor of radius a.

Homework Equations

Ampere's law.
∫B.dl=μI_enclosed

The Attempt at a Solution

Problem has cylindrical symmetry and B is along θ direction.

B*2∏r=μI_enclosed

How to find what fraction of current inside the area considered?

I just saw in a book that it is ∏r²/∏a².But can't figure out the idea.:(

I know it is very simple and donno why i forget basics always..:(

 

[vela]

You have a total current I in the wire. Assume it's evenly distributed across the cross-sectional area of the wire. What would be the current density?

 

[humanist rho]

Yeah!now got it.
Current density is constant.

I_enc/∏r²= I_total/∏α²