Magnetic field

B-field

$\vec{\mathbf{B}}$

• names: magnetic field (ambiguous), magnetic flux density, magnetic induction, B-field
• The SI unit: the tesla ($\mathrm{T}$) which is defined as $1\text{T}=1\text{N}/(\text{A}\cdot \text{m})$

H-field

$\vec{\mathbf{H}}=\frac{1}{{\mu }_0}\vec{\mathbf{B}}-\vec{\mathbf{M}}$

• names: magnetic field intensity, magnetic field strength, magnetic field (ambiguous)
• The SI unit: $A/m$
• ${\mu }_0$ is the permeability of free space
• $\vec{\mathbf{M}}$ is the magnetization of the material
• permeability

Magnetic flux

• ${\Phi }_B={\iint }_S\vec{\mathbf{B}}\cdot d\vec{\mathbf{S}}$ is the magnetic flux (in $\mathrm{Wb}$) through a surface $S$ in a magnetic field $\vec{\mathbf{B}}$.
  • ${\Phi }_B=\vec{\mathbf{B}}\cdot \vec{\mathbf{A}}$ is the magnetic flux through a flat surface with a vector area $\vec{\mathbf{A}}$ in a uniform magnetic field $\vec{\mathbf{B}}$.
  • see also: Gauss’s Law for magnetism

Magnetic moment

• magnetic dipole
• $\vec{\mathbf{\mu }}=I\vec{\mathbf{A}}$ is the magnetic dipole moment (or magnetic moment) (in $\mathrm{A}\cdot {\mathrm{m}}^2$) of a current loop with area $\vec{\mathbf{A}}$ carrying current $I$.
• $\vec{\mathbf{\tau }}=\vec{\mathbf{\mu }}\times \vec{\mathbf{B}}$ is the torque on a magnetic dipole $\vec{\mathbf{\mu }}$ in a magnetic field $\vec{\mathbf{B}}$.
• $U=-\vec{\mathbf{\mu }}\cdot \vec{\mathbf{B}}$ is the potential energy of a magnetic dipole $\vec{\mathbf{\mu }}$ in a magnetic field $\vec{\mathbf{B}}$.