Magnetism And Matter

To determine the magnetic field at a distance from the center of a conducting wire with current flowing through it, we use Ampère's Law. According to Ampère's Law, the line integral of the magnetic field around a closed path is equal to the permeability of free space times the current enclosed by the path:

For a long straight wire, we consider a circular path of radius centered on the wire. The magnetic field is tangent to this circle and has uniform magnitude along the path, so:

Solving for , we find:

This yields the magnetic field at a distance from the center of the wire, where . Hence, the correct expression for the magnetic field is: