The magnetic field
The force on an electric charge depends not only on where it is, but also on how fast it is moving. Every point in space is characterized by two vector quantities which determine the force on any charge. First, there is the electric force, which gives a force component independent of the motion of the charge. We describe it by the electric field, $\FLPE$. Second, there is an additional force component, called the magnetic force, which depends on the velocity of the charge. This magnetic force has a strange directional character: At any particular point in space, both the direction of the force and its magnitude depend on the direction of motion of the particle: at every instant the force is always at right angles to the velocity vector; also, at any particular point, the force is always at right angles to a fixed direction in space (see Fig. 13–1); and finally, the magnitude of the force is proportional to the component of the velocity at right angles to this unique direction. It is possible to describe all of this behavior by defining the magnetic field vector $\FLPB$, which specifies both the unique direction in space and the constant of proportionality with the velocity, and to write the magnetic force as $q\FLPv\times\FLPB$. The total electromagnetic force on a charge can, then, be written as \begin{equation} \label{Eq:II:13:1} \FLPF=q(\FLPE+\FLPv\times\FLPB). \end{equation}  This is called the Lorentz force. The magnetic force is easily demonstrated by bringing a bar magnet close to a cathode-ray tube. The deflection of the electron beam shows that the presence of the magnet results in forces on the electrons transverse to their direction of motion, as we described in Chapter 12 of Vol. I. The unit of magnetic field $\FLPB$ is evidently one newton$\cdot$second per coulomb-meter. The same unit is also one volt$\cdot$second per meter$^2$. It is also called one weber per square meter.