A long wire is known to have a radius greater than 5.6 mm and to carry a current that is uniformly distributed over its cross section. The magnitude of the magnetic field due to that current is 0.44 mT at a point 4.0 mm from the axis of the wire, and 0.27 mT at a point 32 mm from the axis of the wire. What is the radius of the wire?

The radius is

Explanation:

Generally Magnetic field due to a current  carrying wire is is mathematically represented as

Where is the distance from the axis of the wire to the first  point we are considering

            I is the current

              is the permeability of free space

Making I the subject

Generally Magnetic field inside a  current  carrying wire is is mathematically represented as

Now the r here is the distance from the axis of the wire to the second point we are considering

And R i the radius of the wire  

           Making R the subject of the formula

Substituting for I we have

Where B = 0.27mT

And     = 0.44mT

             r = 32mm

              = 4.0mm

Substituting values