Chapter 27 Motion of Charged Particles in a Magnetic Field

1. Chapter 27 Motion of Charged Particles in a Magnetic Field

2. 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).

3. The current I carried by a conductor can be expressed as 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. Microscopic view of electric current Example 27.1 Checkpoint (p.319) O I = nAvQ

4. Q→–veq= 90˚ Q→ +veq= 90˚ q ≠ 90˚ Example 27.2 Experiment 27.1 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 The direction of the force can be determined by Fleming’s left hand rule.

5. Example 27.3 Velocity selector Checkpoint (p.326) O • To pass through the crossed fields in a velocity selector without deflection, the speed of the particles must be

6. 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

7. 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. circular motion q = 90° The centripetal force is provided by the magnetic force acting on the particle:

8. Example 27.4 Mass spectrometer Checkpoint (p.330) O • 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 The radius r differs if the charge to mass ratios (Q / m) differs.

9. 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 conductor with positive charge carriers A conductor with negative charge carriers

10. 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 A conductor with negative charge carriers

11. 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 A conductor with negative charge carriers

12. VH Checkpoint (p.338) O Example 27.5 • 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