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Physics 212 Lecture 12

Physics 212 Lecture 12. Magnetic Force on moving charges. Magnetic Observations. Magnetic Charge?. cut in half. N S. N S. N S. Bar Magnets Compass Needles. N S. N S. S N. N S.

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Physics 212 Lecture 12

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  1. Physics 212 Lecture 12 Magnetic Force on moving charges

  2. Magnetic Observations Magnetic Charge? cut in half N S N S N S • Bar Magnets • Compass Needles N S N S S N N S N S 07

  3. Magnetic Observations V V V V I F I F F I I F • Compass needle deflected by electric current I • Magnetic fields created by electric currents • Magnetic fields exert forces on electric currents (charges in motion) 12

  4. Magnetism & Moving Charges Lorentz Force Biot-Savart Law All observations are explained by two equations: 14

  5. Cross Product Review • Cross Product different from Dot Product • A●Bis a scalar; A x B is a vector • A●Bproportional to the component of B parallel to A • A x B proportional to the component of B perpendicular to A • Definition of A x B • Magnitude: ABsinq • Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule 16

  6. Remembering Directions: The Right Hand Rule y x F B qv z 17

  7. Checkpoint 1a Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: A B C D E The particle’s velocity is zero. There can be no magnetic force. 18

  8. qv X B F Checkpoint 1b Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: A B C D E 21

  9. Cross Product Practice • Positive charge coming out of screen • Magnetic field pointing down • What is direction of force ? A) Left B) Right C) UP D) Down E) Zero + y - y - x + x y x B screen z 24

  10. is constant But can change ! B field cannot change kinetic energy of a charge. No work done by B field  Kinetic energy is constant

  11. q q q q constant v x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x F F Centripetal acceleration: v v F F v Cyclotron Motion – uniform B field R Solve for R: UniformBinto page 30

  12. LHC 17 miles diameter

  13. qv . F B Checkpoint 2a The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. A B C D 34

  14. Checkpoint 2b The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. A B C Observation: R2 > R1 36

  15. Calculation exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Calculate v, the velocity of the particle as it enters the magnetic field • Use Lorentz Force equation to determine the path in the field as a function of B • Apply the entrance-exit information to determine B

  16. Calculation • What is v0, the speed of the particle as it enters the magnetic field ? (A) (B) (C) (D) (E) exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Why?? • Conservation of Energy • Initial:Energy =U = qV = qEd • Final: Energy = KE = ½ mv02 • Newton’s Laws • a = F/m = qE/m • v02 = 2ad

  17. Calculation • What is the path of the particle as it moves through the magnetic field? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X (A) (B) (C) exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Why?? • Path is circle ! • Force is perpendicular to the velocity • Force produces centripetal acceleration • Particle moves with uniform circular motion

  18. Calculation • What is the radius of path of particle? (A) (B) (C) (D) (E) R xo/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Why??

  19. Calculation (A) (B) (C) (D) (E) exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Why??

  20. Follow-Up (A) (B) (C) exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? 1. q changesv changes Several things going on here 2. q & v changeF changes 3. v & F changeR changes

  21. Follow-Up How does v, the new velocity at the entrance, compare to the original velocity v0? (A) (B) (C) (D) (E) exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? • Why??

  22. Follow-Up How does F, the magnitude of the new force at the entrance, compare to F0, the magnitude of the original force? (A) (B) (C) (D) (E) exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? • Why??

  23. Follow-Up How does R, the radius of curvature of the path, compare to R0, the radius of curvature of the original path? (A) (B) (C) (D) (E) exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? • Why??

  24. Follow-Up exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E q,m x0 d enters here B B • Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? (A) (B) (C)

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