Loi d'Ampère : Résolution de problème

Consider an infinite straight, thick conductor carrying a uniform current. What is the magnetic field inside and outside the conductor?

Here, the current distribution possesses a cylindrical symmetry, and the circular magnetic field lines are concentric with the conductor axis.

To estimate the field inside the conductor, consider an Amperian loop with a radius less than the conductor radius.

The line integral of the magnetic field along this loop equals the magnetic field times the circumference. The current enclosed by the loop equals the product of current density and the enclosed area.

Thus, using Ampere's Law, the magnetic field inside the conductor is obtained.

For an Amperian loop with a radius greater than the conductor radius, the current enclosed by the loop equals the current flowing through it.

Again, applying Ampere's Law, the magnetic field outside the conductor is inversely proportional to the loop radius.

The magnitude of the magnetic field inside the conductor increases linearly till it reaches a maximum value at its radius. Outside the conductor, the field magnitude drops inversely with distance.