The magnetic field in a region of space centered on the origin has cylindrical symmetry and is given by b~ = b0φˆ where b0 is a constant and φˆ is the azimuthal direction in cylindrical coordinates. what is the current density in this region of space?

To solve this problem, the application of the Ampere law is necessary.

This law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.

The equation is defined as,

Where,

B= Magnetic field

Permeability constant

J = Total current density

r = Radius

Integrating we have:

Therefore with that condition the previous equation represent the current density in this region of space

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