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Electricity and Magnetism Chapter 27 Motion of Charged Particles in a Magnetic Field 27 Motion of Charged Particles in a Magnetic Field Electricity and Magnetism • In the presence of electric field, the electrons experience electric forces and drift slowly in the opposite direction of the electric field at the drift velocity. • The drift velocity (~10–5 m s–1) of free electrons is extremely small compared with their mean speed (~106 m s–1). 27 Motion of Charged Particles in a Magnetic Field Electricity and Magnetism • The current I carried by a conductor can be expressed as I = nAvQ where n is the number of free charge carriers per unit volume; A is the cross-sectional area of the conductor; v is the drift velocity of the charge carriers; Q is the charge carried by the charge carriers. Example 27.1 27 Microscopic view of electric current Checkpoint (p.319) O Motion of Charged Particles in a Magnetic Field Electricity and Magnetism 27.2 Magnetic force on a moving charge • The magnetic force F on a moving charged particle with a velocity v in a magnetic field B at an angle q is given by F = BQv sin q ≠ 90˚ Q →q +ve –ve q = 90˚ The direction of the force can be determined by Fleming’s left hand rule. Example 27.2 Experiment 27.1 27 Motion of Charged Particles in a Magnetic Field Electricity and Magnetism • To pass through the crossed fields in a velocity selector without deflection, the speed of the particles must be E v B Velocity selector 27 Example 27.3 Checkpoint (p.326) O Motion of Charged Particles in a Magnetic Field Electricity and Magnetism Motions of charged particles in uniform magnetic field • The motion of a charged particle in a uniform magnetic field B depends on the angle q between its initial velocity v and the direction of the field. q = 0° or 180° F=0 rectilinear motion 27 Motion of Charged Particles in a Magnetic Field Electricity and Magnetism • The motion of a charged particle in a uniform magnetic field B depends on the angle q between its initial velocity v and the direction of the field. q = 90° circular motion The centripetal force is provided by the magnetic force acting on the particle: mv 2 BQv r mv r QB 27 Motion of Charged Particles in a Magnetic Field Electricity and Magnetism • In a mass spectrometer, the radii of the semi-circular paths taken by the charged particles depend on their charge to mass ratios, so that different particles can be separated and identified. Recall that the radius r of the circular path is given by mv r QB The radius r differs if the charge to mass ratios (Q / m) differs. Mass spectrometer 27 Example 27.4 Motion of Charged Particles in a Magnetic Field Checkpoint (p.330) O Electricity and Magnetism 27.3 Hall effect Deflection of charge carriers in conductor • When a current passes through a conductor placed in a uniform magnetic field, each of the charge carriers experiences a magnetic force and deflects to the surfaces. A A conductor conductor with with negative positive charge charge carriers carriers 27 Motion of Charged Particles in a Magnetic Field Electricity and Magnetism • The deflection of the moving charged carriers leads to – an excess of positive (or negative) charge carriers on the upper surface, and – a deficiency of positive (or negative) charge carriers on the lower surface. A conductor with positive charge carriers 27 A conductor with negative charge carriers Motion of Charged Particles in a Magnetic Field Electricity and Magnetism Hall voltage • A p.d. is developed across the conductor due to the deflected charge carriers. • Each charge carrier moving in the conductor experiences an electric force that opposes the magnetic force on it. • These two forces balance each other in the steady state. A conductor with positive charge carriers 27 A conductor with negative charge carriers Motion of Charged Particles in a Magnetic Field Electricity and Magnetism • The Hall effect is the production of a Hall voltage across the opposite surfaces of a current-carrying conductor placed in a magnetic field, which is given by BI VH nQb VH Checkpoint (p.338) O 27 Example 27.5 Motion of Charged Particles in a Magnetic Field