Physical Basis For The Rules
When electrons, or indeed any charged particles, flow in the same direction (for example, as an electric current in an electrical conductor, such as a metal wire) they generate a cylindrical magnetic field that wraps round the conductor (as discovered by Hans Christian Ørsted).
The direction of the induced magnetic field is sometimes remembered by Maxwell's corkscrew rule. That is, if the conventional current is flowing away from the viewer, the magnetic field runs clockwise round the conductor, in the same direction that a corkscrew would have to turn in order to move away from the viewer. The direction of the induced magnetic field is also sometimes remembered by the right-hand grip rule, as depicted in the illustration, with the thumb showing the direction of the conventional current, and the fingers showing the direction of the magnetic field. The existence of this magnetic field can be confirmed by placing magnetic compasses at various points round the periphery of an electrical conductor that is carrying a relatively large electric current.
If an external magnetic field is applied horizontally, so that it crosses the flow of electrons (in the wire conductor, or in the electron beam), the two magnetic fields will interact. Michael Faraday introduced an analogy for visualising this, in the form of imaginary magnetic lines of force: those in the conductor form concentric circles round the conductor; those in the externally applied magnetic field run in parallel lines above and below the conductor. If those above the conductor are running (from the north to south magnetic pole) in the opposite direction to those surrounding the conductor, they will be deflected so that they pass underneath the conductor (because magnetic lines of force cannot cross or run contrary to each other). Consequently, there will be a large number of magnetic field lines in a small space under the conductor, and a dearth of them above the conductor. Since the magnetic field lines of force are no longer straight lines, but curved to run under the electrical conductor, they are under tension (like stretched elastic bands), with energy stored up in the magnetic field. There is therefore a force that is being applied to the only moveable object in the system (the electrical conductor) to expel it up, and out of the externally applied magnetic field. This is the reason for torque in an electric motor. (The mechanism of the electric motor is then constructed so that the expulsion of the conductor out of the magnetic field causes it be placed inside the next magnetic field, and for this switching to be continued indefinitely.)
Faraday's Law; The induced emf in a conductor is directly proportional to the rate of change of the magnetic flux in the conductor.
Read more about this topic: Fleming's Left-hand Rule For Motors
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