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A long, hollow cylinder with inner radius R1 and outer radius R2 carries current along its...

A long, hollow cylinder with inner radius R1 and outer radius R2 carries current along its length. The current is uniformly distributed over the cross-sectional area of the cylinder and has current density J.

1. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points inside the hollow interior (r<R1). Express your answer in terms of the variables R1, R2, J, and r.

2. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points inside the solid conductor (R1<r<R2). Express your answer in terms of the variables R1, R2, J, and r.

3. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points outside the conductor (r>R2).

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Answer #1

Current enclosed in the Cylinder is  is

Ampere's law

1)

Inside the hollow interior of cylinder,

Charge enclosed in hollow region of cylinder is zero,

2)

For the amperean loop inside the solid conductor,

Charge enclosed is

3)

For the amperean loop outside the conductor,

Charge enclosed is

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