2. When the initial velocity is perpendicular to the magnetic field: Figure shows a magnetic field directed normally into the plane of paper, as shown by small crosses. B A charge projected with a speed in the plane of the paper. The velocity is perpendicular to the +qis v magnetic field. A force acts on the particle perpendicular to F = qvB both and . This force continuously deflects the particle sideways without changing its v B speed and the particle will move along a circle perpendicular to the field. Thus the magnetic force provides the centripetal force. Let be the radius of the circular path. r mv2 Centripetal force, = Magnetic force, qvB r mv = r qB mv m Period of revolution, T= . v v qB qB 1 qB The frequency of revolution is f c T m This frequency is independent of and and is called cyclotron frequency. v r 3. When the initial velocity makes an arbitrary angle with the field direction: Consider a charged particle entering a uniform magnetic field with velocity q B inclined at an angle with the direction of ,as shown in figure. B
2. When the initial velocity is perpendicular to the magnetic field: Figure shows a magnetic field B directed normally into the plane of paper, as shown by small crosses. A charge +qis projected with a speed v in the plane of the paper. The velocity is perpendicular to the magnetic field. A force F = qvB acts on the particle perpendicular to both v and B . This force continuously deflects the particle sideways without changing its speed and the particle will move along a circle perpendicular to the field. Thus the magnetic force provides the centripetal force. Let r be the radius of the circular path. Centripetal force, mv2 = Magnetic force, qvB r r = mv qB Period of revolution, T= . mv v v qB qB The frequency of revolution is f c 1 qB T This frequency is independent of v and r and is called cyclotron frequency. 3. When the initial velocity makes an arbitrary angle with the field direction: Consider a charged particle q entering a uniform magnetic field B with velocity inclined at an angle with the direction of B ,as shown in figure. m m
physics-xii-15-16.docx