. M OTION IN A M AGNETIC F IELD We will now consider, in greater detail, the motion of a charge moving in a magnetic field. We have learnt in Mechanics (see Class XI book, Chapter ) that a force on a particle does work if the force has a component along (or opposed to) the direction of motion of the particle. In the case of motion E XAMPLE .
Charged particles moving in a magnetic field. Interactive demonstration: of a charge in a magnetic field, the magnetic force is perpendicular to the velocity of the particle. So no work is done and no change in the magnitude of the velocity is produced (though the direction of momentum may be changed). [Notice that this is unlike the force due to an electric field, q E , which can have a component parallel (or antiparallel) to motion and thus can transfer energy in addition to momentum.] We shall consider motion of a charged particle in a uniform magnetic field.
First consider the case of v perpendicular to B . The perpendicular force, q v × B , acts as a centripetal force and produces a circular motion perpendicular to the magnetic field. The particle will describe a circle if v and B are perpendicular to each other (Fig. .
). If velocity has a component along B , this component remains unchanged as the motion along the magnetic field will not be affected by the magnetic field. The motion in a plane perpendicular to B is as before a circular one, thereby producing a helical motion (Fig. .
). You have already learnt in earlier classes (See Class XI, Chapter ) that if r is the radius of the circular path of a particle, then a force of m v / r , acts perpendicular to the path towards the centre of the circle, and is called the centripetal force. If the velocity v is perpendicular to the magnetic field B, the magnetic force is perpendicular to