The concepts used to solve this problem are magnetic field due to a current-carrying wire.
Use the relation between magnetic field due to a current-carrying wire, radial distance, and permeability of free space to find the maximum current in the wire.
The Ampere’s law states that “for any closed loop, the sum of the length elements multiples the magnetic field in the direction of the length element and is equal to the permeability times the electric current enclosed in the closed loop path.
Expression for the magnetic field due to current carrying wire is

Here, the magnetic field is
, the radial distance is
, the permeability of free space is
, and the current is
.
Expression for the magnetic field due to a current-carrying wire is

Rearrange the above equation to get 

Expression for the maximum current in the wire is

Substitute
for
,
for
, and
for
.

The maximum current in the wire is
.
If an electric wire is allowed to produce a magnetic field no larger than that of...
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