Electromagnetism

A magnetic field is a region in which a moving charge or a magnet experiences a force, and it is set up by moving charges, not by a charge at rest and not by an isolated magnetic pole. We picture it with field lines, which are imaginary lines that stand for a real field: outside a magnet they leave the north pole and return to the south pole, they never cross, and their density shows the strength.

Magnetic flux density, $B$, also called the magnetic induction or the magnetic field strength, is the flux through unit area placed perpendicular to the field, $B = \Phi_B/A$; its unit is the tesla, which is also $\text{Wb},\text{m}^{-2}$ and $\text{N},\text{A}^{-1},\text{m}^{-1}$. Magnetic flux, $\Phi_B$, is the total field through a surface and is the scalar product $\Phi_B = \mathbf{B}\cdot\mathbf{A} = BA\cos\theta$, where $A$ points along the normal and $\theta$ is the angle between the field and the normal. Because it is a dot product, flux is a scalar with a unit but no direction, and its unit is the weber, $1\ \text{Wb} = 1\ \text{N},\text{m},\text{A}^{-1} = 1\ \text{J},\text{A}^{-1}$. Flux is greatest, $BA$, when the field runs along the normal ($\theta = 0^\circ$) and zero when the field lies in the plane of the surface ($\theta = 90^\circ$), and it depends on the area, the field and the orientation, not on the shape of the surface.