Forces in a magnetic field
When a current-carrying conductor is positioned inside and at right angles to a magnetic field the current is found to experience a force. The equation to caluculate the magnitude of the force is F=BIl where F is force in Newtons, B is the strength of the magnetic field in teslas, I is the current in amps and l is the length of the conductor in metres.
Flemings left hand rule
Flemings left hand rule is a tool used by physicists in order to deduce the direction of the force that acts on a conductor in a magnetic field. The thumb on the hand indicates the force, the index finger represents the direction of the magnetic field and the middle finger represents the direction of the current. Flemings left hand rule is only a tool for remembering these facts, it has nothing to do with the physics behind the force.
Charged Particles
Charged particles moving through a vacuum represent a flow of charge like electrons do when moving through a conductor. This means that when these particles are moving at right angles to a magnetic field they will experience a force and the direction of this force can be determined by flemings left hand rule. The magnitude of a force on a particle with charge Q, travelling with a velocity v in a magnetic field of strength B is given by F=BQv
When a charged particle moves in a uniform magnetic field it will experience a force at different postions and this will cause it to move in a circular way due to the forces experienced by the particles at the postions that it is deviated to. The circle formed has a radius r, and in this case the magnetic field is providing the centripetal force so, BQv=mv(squared)/r. Cancelling v gives the radius r=mv/BQ.
Demonstrating the magnetic force on an electron
An electron beam can be deflected by a magnetic field when it is travelling vertically and this causes it to be deflected into a circular path. The magnetic field is produced by Helmholtz coils (these are a pair of large coils that fit in a holder so they are symmetrically positioned around electron tubes like the fine beam or deflection tubes).The coils provide a uniform magnetic field with strength B that can be calculated by a formula. By measuring the accelerating voltage, the radius of the circle in which the electrons travel and the magnetic field strength a value for the specific charge on an atom can be calculated.