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

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To find the magnetic field inside a long conductor of radius a, Ampere's law is applied, leading to the equation B*2∏r=μIenclosed. The problem involves cylindrical symmetry, with the magnetic field B directed along the θ direction. To determine the enclosed current, the fraction of the total current within the area considered must be calculated, which is derived from the ratio of the areas: ∏r²/∏a². The current density is assumed to be constant across the conductor's cross-section, allowing for the relationship Ienc/∏r²= Itotal/∏a² to be established. Understanding these concepts clarifies how to compute the magnetic field effectively.
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Homework Statement


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


Homework Equations


Ampere's law.
∫B.dl=μIenclosed


The Attempt at a Solution



Problem has cylindrical symmetry and B is along θ direction.

B*2∏r=μIenclosed

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..:(
 
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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?
 
Yeah!now got it.
Current density is constant.

Ienc/∏r2= Itotal/∏α2
 

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