1. The problem statement, all variables and given/known data A current of constant density, J0, flows through a very long cylindrical conducting shell with inner radius a and outer radius b. What is the magnetic field in the regions r < a, a < r < b, and r > b? (Use any variable or symbol stated above along with the following as necessary: μ0.) 2. Relevant equations Ampere's Law [itex]\oint B \bullet ds[/itex] = μ0ienc 3. The attempt at a solution [itex]\oint B \bullet ds[/itex] = μ0ienc Solving for B: B[itex]\oint ds[/itex] = μ0ienc B2∏r = μ0ienc B = μ0ienc/2∏r At r < a: B = 0 because ienc at this point = 0 At a < r < b: B = μ0ienc/2∏r I don't know how to get ienc. I know it has something to do with the current density. At r > b: ienc = itotal, but I would need an expression for the volume of the cylinder. V = ∏b2h - ∏a2h V = ∏h(b2-a2) Ienc = J0V [itex]\Rightarrow[/itex] Ienc = J0∏h(b2-a2) B = μ0ienc/2∏r B = μ0J0h(b2-a2)/2r However, by including h, I am introducing variables that the problem hasn't allowed me to use.