Chapter 29 Magnetic Fields

1. Chapter 29 Magnetic Fields PHYS 2326-16

2. Concepts to Know • Permanent Magnets • Magnetic Poles • N-Pole (north seeking) • S-Pole (south seeking) • Magnetic Field

3. Concepts to Know • Magnetic field lines • Magnetic Monopole (never found) • Magnetic force on moving charge • Cyclotron frequency • Velocity selector • Mass spectrometer

4. Magnetic Field • Vector B represents the magnetic field with a direction from N-pole to S-pole • Unit is Tesla • alternate unit is Gauss = 10-4 typical earth field 0.5 Gauss • North pole of magnets attracted earth’s north pole which is opposite polarity

5. Units • 1 Tesla = 1 N/(Coulomb meter/s) • a Coulomb/second is an ampere so • 1 T = 1 N/(A m) • 10^4 Gauss (G) = 1 Tesla (T)

6. Magnetic Force on Moving Charge

7. Electromagnetic Force • on a moving charge

8. Electric & Magnetic Force Differences • Force for electric field is along the direction of the field line, force for magnetic field is perpendicular to the field • Electric field force operates on any charge, Magnetic field force acts only on moving charge • Electric field performs work when displacing charged particle, Magnetic field moves charges perpendicular to displacement performing no work.

9. Right Hand Rule

10. Right Hand Rule • Cross product reverses sign when reverse vectors = v x B = -B x v • Result is perpendicular to the plane that contains v and B. • Direction for result F is the same as a screw moves when rotated in the direction from v to B (clockwise moves screw in and CCW moves screw out

11. Charged Particle in Uniform Field • Magnetic force F is perpendicular to v and B • Has constant magnitude qvB. • Motion is in a circle for uniform B and no other forces acting on the moving charged particle • centripetal acceleration = mv^2/r • r = mv/qB (top is momentum) eqn 29.3 • ω = v/r = qB/m = angular speed • T=2πr/v = 2 π/ ω = 2 πm/ qB = period

12. Cyclotron Frequency • Cyclotron frequency is ω the angular speed • A cyclotron is an essentially obsolete particle accelerator – mostly now used in nuclear medicine. • If there is a velocity component parallel to B there is no effect on the particle due to this component and the path becomes a helix

13. Cyclotron • Atom smasher • Hollow cylinder in 2 insulated halves with a uniform magnetic field along the cylinder axis. • Particles released near the center • The two halves flip flop an E field drawing particles from one side to the other and back – imparting kinetic energy each time qV • Particle spirals out with increased speed • Exits when fast enough to reach exit point

14. Velocity Selector • An apparatus where there is an electric field perpendicular to a magnetic field and both perpendicular to the initial motion of a stream of charged particles one can create a velocity selector. • FB = qvB (direction = right hand rule) • FE = qE (direction = E) • FB = - FE (- is opposite directions) • qE = qvB so that v = E/B (magnitude) • Particles with velocity v go through undeflected, others are diverted

15. Mass Spectrometer • Separates ions according to mass / charge ratio • Bainbridge mass spec. beam enters a velocity separator then through a perpendicular magnetic field B • Ions move in semicircle striking the detector at a point P. Negative ions are deflected one way, positive the other.

16. Mass Spectrometer Equations • Starting with 29.3 the radius eqn r=mv/qBo for uniform and perpendicular motion and Bo field. • m/q = Bo r/v by rearranging • substituting 29.7 the velocity selector equation, v=E/B • m/q = r Bo B/E