1. Physics 212 Lecture 12, Slide 1 Physics 212 Lecture 12 Magnetic Force on moving charges

2. Physics 212 Lecture 12, Slide 2 Magnetic Observations N S Bar Magnets Compass Needles S N N S cut in half 07 N S Magnetic Charge?

3. Physics 212 Lecture 12, Slide 3 Compass needle deflected by electric current I Magnetic fields created by electric currents Magnetic fields exert forces on electric currents (charges in motion) V V I I F F V V I I F F Magnetic Observations 12

4. Physics 212 Lecture 12, Slide 4 Magnetism & Moving Charges All observations are explained by two equations: Lorentz Force 14 Biot-Savart Law

5. Physics 212 Lecture 12, Slide 5 Cross Product Review Cross Product different from Dot Product –A ● B is a scalar; A x B is a vector –A ● B proportional 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: ABsin  –Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule 16

6. Physics 212 Lecture 12, Slide 6 Remembering Directions: The Right Hand Rule x y z B F qv 17

7. Physics 212 Lecture 12, Slide 7 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: Checkpoint 1a The particle’s velocity is zero. There can be no magnetic force. 18 ABCDEABCDE

8. Physics 212 Lecture 12, Slide 8 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: ABCDEABCDE 21 X qv B F Checkpoint 1b

9. Physics 212 Lecture 12, Slide 9 Cross Product Practice Positive charge coming out of screen Magnetic field pointing down What is direction of force ? A) LeftB) RightC) UPD) Down E) Zero screen x y z B 24 - x + x + y - y

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

11. Physics 212 Lecture 12, Slide 11 x x x x x x x Uniform B into page q v F q v F q v F q v F R 30 Solve for R: Cyclotron Motion – uniform B field constant Centripetal acceleration:

12. Physics 212 Lecture 12, Slide 12 LHC 17 miles diameter

13. Physics 212 Lecture 12, Slide 13 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. Checkpoint 2a 34 qv F B. BACD

14. Physics 212 Lecture 12, Slide 14 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. Observation: R 2 > R 1 36 Checkpoint 2b ABCABC

15. Physics 212 Lecture 12, Slide 15Calculation 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 x 0 are known. What is 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 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 B B x 0 /2 exits here enters here d q,m x0x0 E

16. Physics 212 Lecture 12, Slide 16Calculation 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m Why?? –Conservation of Energy Initial: Energy = U = qV = qEdInitial: Energy = U = qV = qEd Final: Energy = KE = ½ mv 0 2Final: Energy = KE = ½ mv 0 2 –Newton’s Laws a = F/m = qE/ma = F/m = qE/m v 0 2 = 2adv 0 2 = 2ad x0x0 E What is v 0, the speed of the particle as it enters the magnetic field ? (A) (B) (C) (D) (E)

17. Physics 212 Lecture 12, Slide 17Calculation 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m Why?? –Path is circle ! Force is perpendicular to the velocityForce is perpendicular to the velocity Force produces centripetal accelerationForce produces centripetal acceleration Particle moves with uniform circular motionParticle moves with uniform circular motion x0x0 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 What is the path of the particle as it moves through the magnetic field? (A) (B) (C) 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 E

18. Physics 212 Lecture 12, Slide 18Calculation 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m Why?? x0x0 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 R x o /2 E What is the radius of path of particle? (A) (B) (C) (D) (E)

19. Physics 212 Lecture 12, Slide 19Calculation 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m Why?? x0x0 E (A) (B) (C) (D) (E)

20. Physics 212 Lecture 12, Slide 20Follow-Up 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m x0x0 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) E Several things going on here 1. q changes  v changes 2. q & v change  F changes 3. v & F change  R changes

21. Physics 212 Lecture 12, Slide 21Follow-Up 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? How does v, the new velocity at the entrance, compare to the original velocity v 0 ? Why?? E (A) (B) (C) (D) (E)

22. Physics 212 Lecture 12, Slide 22Follow-Up 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? How does F, the magnitude of the new force at the entrance, compare to F 0, the magnitude of the original force? Why?? E (A) (B) (C) (D) (E)

23. Physics 212 Lecture 12, Slide 23Follow-Up 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? How does R, the radius of curvature of the path, compare to R 0, the radius of curvature of the original path? Why?? E (A) (B) (C) (D) (E)

24. Physics 212 Lecture 12, Slide 24Follow-Up 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 x 0 are known. What is B? 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 B B x 0 /2 exits here enters here d q,m x0x0 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) E