B field inside conductor with assymetric cavity

AI Thread Summary
To determine the B-field inside a cylindrical cavity of a conductor carrying a current, the relevant equation is the line integral of the magnetic field, given by ∮B·dl = μ₀I. The discussion emphasizes the need to perform an outer line integral around the conductor and then subtract the inner line integral for the cavity. Participants are seeking clarification on whether this approach is correct and how to effectively compute the inner line integral. The focus is on understanding the magnetic field's direction and magnitude within the cavity. The conversation highlights the importance of applying Ampère's law in this context.
Gauss M.D.
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Homework Statement



Infinite straight conductor, parallel with z axis, of radius R1 with a cylindrical cavity of radius R2. The axis of the cavity passes through the point <0,b,0>. A current I flows through the conductor. The current density is homogenous inside the cundoctor. Find the direction and magnitude of the B-field inside the cavity.

Homework Equations





The Attempt at a Solution



I think we're supposed to use

\oint \textbf{B} \cdot \textbf{dl} = \mu _0 I

Where we first do the outer line integral, and then subtract the inner line integral.

1) Am I on to something?
2) How do I do the inner line integral in the most convenient way?
 
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