If an electric wire is allowed to produce a magnetic field no larger than that of the earth (0.50×10−4t) at a distance of 12 cm from the wire, what is the maximum current the wire can carry

The magnetic field generated by a wire carrying a current I is:

where r is the distance at which the magnetic field is measured, and  is the magnetic permeability in vacuum.

The problem says that the magnetic field at a distance r=12 cm=0.12 m from the wire must be no larger than . Substituting these values, we can find the maximum value of the current I that the wire can carry:

By dividing you can find the answer