The magnetic field and the tesla

There exists a vector quantity, the magnetic field $\vec{B}$, such that in the presence of a magnet (or a current) other magnets (or moving charges) experience forces. It is the magnetic analogue of the electric field $\vec{E}$: it describes, point by point, how space is disposed to exert magnetic forces.

Principle — The magnetic field $\vec{B}$

In the presence of a magnet or a current, other moving charges experience a force described by the vector field $\vec{B}$. Its magnitude is measured in tesla (T).

The unit of measurement of the magnetic field is the tesla (T). Analysing the Lorentz force $F = qvB$ dimensionally gives the equivalence in base units:

$1\;\text{T} = 1\;\frac{\text{kg}}{\text{A}\cdot\text{s}^2}$

The tesla is a “large” unit: the Earth’s magnetic field at the surface is about $5\cdot 10^{-5}\;\text{T}$, a common fridge magnet a few millitesla, while the superconducting magnets of an MRI scanner reach $1$–$3\;\text{T}$.

Alongside $\vec{B}$ there is a fundamental constant, the magnetic permeability of free space $\mu_0$, the magnetic analogue of $\varepsilon_0$ in electrostatics:

$\mu_0 = 4\pi\cdot 10^{-7}\;\text{T}\cdot\text{m/A}$

The relation that unifies electricity and magnetism

$\varepsilon_0\,\mu_0 = \frac{1}{c^2}$ The electric and magnetic constants are not independent: their product fixes the speed of light. This is the first clue that light, electricity and magnetism are the same phenomenon, as will become clear with Maxwell’s equations.

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Topics: Magnetismo Concepts: Campo magnetico

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