A long, hollow wire with inner radius a and outer radius b carries a uniform current density J. What is the magnetic field as a function of r, the distance from the center of the wire within the wire's material (i. e. what is B(r) in the region a < r < b)?

The magnetic field in the region a < r < b is

Explanation:

If we have the a < r < b. The formula of current is:

Where:

A = area enclosed by the loop.

Itotal = total current in loop.

If we have the Ampere`s law:

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explanation: