Magnetic field

The magnetic field ($\vec{H}$) is a vector field, generated by a current-carrying wire at a position in space. The magnetic flux density ($\vec{B}$) is measured in teslas ($\frac{N}{C\cdot \frac{m}{s}}$), proportional to the magnetic field intensity.

$$\vec{B}=\mu \vec{H}$$

where $\mu$ is the permeability constant of the medium.

We can compute the magnetic field and flux density using the Biot-Savart law or Ampere’s law (where there’s symmetry).

Properties

A fundamental postulate of magnetism is that magnetic flux lines are always closed. From the below relations for the divergence/curl of a magnetic field, we conclude that there’s no magnetic point source (the same way there is for electric charge). We cannot isolate a magnetic monopole, so a material will function as a source and sink and not either; magnets only exist as dipoles.

Gauss’ law for magnetism states that:

$$\oint {\oint }_S\vec{B}\cdot d\vec{S}=0$$ $$\nabla \cdot \vec{B}=0$$

Ampère’s law states that:

$$\nabla \times \vec{B}={\mu }_0\vec{J}$$

An oscillating electric field produces a perpendicular oscillating magnetic field, both at the speed of light in a vacuum. They’re collectively called electromagnetic waves, and are transverse waves.

See also

• Electric field
• Gravitational field
• Magnetism