Magnetic Field Explorer

The Biot-Savart Law gives the magnetic field produced by a small current element. It is the magnetic analog of Coulomb's Law.

where $\mu_0 = 4\pi \times 10^{-7} \text{ T\cdot m/A}$ is the permeability of free space. The cross product means $d\vec{B}$ is always perpendicular to both the current element and the displacement vector.

Integrating the Biot-Savart Law (or using Ampere's Law with a circular Amperian loop) gives the magnetic field at perpendicular distance r from an infinite wire carrying current I.

The field lines form concentric circles around the wire. The direction is determined by the right-hand rule: point your thumb in the direction of current, and your fingers curl in the direction of the field.

On the axis of a circular loop of radius R carrying current I, the magnetic field at distance x from the center is:

At the center ($x = 0$), this simplifies to $B = \frac{\mu_0 I}{2R}$. The field pattern resembles a magnetic dipole (bar magnet) far from the loop.

A solenoid with N turns over length L produces a nearly uniform magnetic field inside. Using Ampere's Law with a rectangular loop:

The field at the ends is half the interior value: $B_{\text{end}} = \frac{\mu_0 n I}{2}$. Outside an ideal, infinitely long solenoid, the field is approximately zero.