Explanation:
Given that,
Radius a= 5.0 mm
Radial distance r= 0, 2.9 mm, 5.0 mm
Current density at the center of the wire is given by

Given relation between current density and radial distance

We know that,
When the current passing through the wire changes with radial distance,
then the magnetic field is induced in the wire.
The induced magnetic field is
...(I)
We need to calculate the induced current
Using formula of induced current




We need to calculate the magnetic field
Put the value of induced current in equation (I)


(a). The magnetic field at a distance r = 0
Put the value into the formula


The magnetic field at a distance 0 is zero.
(b). The magnetic field at a distance r = 2.9 mm


The magnetic field at a distance 2.9 mm is 
(c). The magnetic field at a distance r = 5.0 mm


The magnetic field at a distance 5.0 mm is 
Hence, This is the required solution.