2. Review, Sunday Feb. 17 3 PM, 141 Loomis I will go over a past exam Vote for which exam a)Fall 2007 b)Spring 2007 c)Fall 2006 d)Spring 2006 e)Fall 2005 Physics 102: Lecture 08

3. Today’s Lecture: Magnetism This material is NOT on exam 1 Magnetic fields Magnetic force on charged particles

4. Magnets are Cool! +- North Pole and South Pole –Opposites Attract –Likes Repel Lets Break it! Magnetic Field Lines –Arrows give direction –Density gives strength –Looks like dipole! 15

5. S N Field Lines of Bar Magnet Magnetic field lines don’t start or stop. There are no magnetic charges (monopoles) 18

6. S N 3 2 1 Preflight 8.1 Which drawing shows the correct field lines for a bar magnet? (1) 10% (2) 30% (3) 60% Magnetic field lines are continuous Arrows go from N to S outside the magnet (S to N inside).

7. S N The Earth is a Magnet

8. Comparison: Electric Field Lines vs. Magnetic Field Lines Similarities –Density gives strength –Arrow gives direction Leave +, North Enter -, South Differences –Start/Stop on electric charge –No Magnetic Charge, lines are continuous! FYI –x x x x x x x INTO Page – OUT of Page 20

9. No Magnetic Charges Magnetic Fields are created by moving electric charge! Where is the moving charge? Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) 21

10. Magnetic Fields and Forces Magnetic fields exert forces on moving charge We will discuss the magnitude of the force shortly Direction of force is given by a “right-hand rule”

11. Direction of Magnetic Force on Moving Charges 25 Magnetic force is perpendicular to both B and v Right-hand rule: –Thumb of right hand points in v direction –Orient hand so that forefinger points in B direction –Then normal to palm points in direction of F Outward normal for + charge Opposite for – charge 25 v B F

12. Direction of Magnetic Force on Moving Charges VelocityBForce out of page right up out of page left down 25 ACT: 1) Up 2) Down 3) Right 4) Left 5) Zero out of page up v B F

13. Direction of Magnetic Force on Moving Charges VelocityBForce out of page right up out of page left down out of page up out of page down 25 right left v B F

14. Preflight 8.3 What is the direction of the force on the particle just as it enters region 1? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. Particle is moving straight upwards then veers to the right. 27 21% 7% 9% 30% 24% 9%

15. Preflight 8.4 What is the direction of the magnetic field in region 1? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC 17% 6% 8% 22% 20% 26% 27 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. _ _ v (thumb) points up, F(palm) points right: so B(fingers) must point out.

16. ACT: 2 Chambers What is the direction of the magnetic field in region 2? A) down B) left C) right D) into page E) out of page 1 2 v = 75 m/s q = +25 mC v (thumb) points right, F(palm) points up, B(fingers) point in. 29 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.

17. The magnetic force on a charge depends on the magnitude of the charge, its velocity, and the magnetic field. F = q v B sin(  ) –Direction from RHR Thumb (v), fingers (B), palm (F) –Note if v is parallel to B then F=0 B  V Magnitude of Magnetic Force on Moving Charges 30

18. ACT: Moving Charges The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. 1) Which particle experiences the greatest magnetic force? A) 1B) 2C) 3D) All Same 2) The force on particle 3 is in the same direction as the force on particle 1. A) TrueB) False B 1 2 3 F = q v B sin(  ) Thumb (v), fingers (B), palm (F) into page! 33

19. Comparison Electric vs. Magnetic ElectricMagnetic Source: ChargesMoving Charges Act on: Charges Moving Charges Magnitude: F = Eq F = q v B sin(  ) Direction: Parallel to EPerpendicular to v,B 34

20. Velocity Selector Determine magnitude and direction of magnetic field such that a positively charged particle with initial velocity v travels straight through and exits the other side. v E For straight line, need |F E |= |F B | q E= q v B sin(90) B = E/v What direction should B point if you want to select negative charges? A) Into PageB) Out of pageC) Left D) Right 38 F E would be up so F B must be down. FEFE FBFB Electric force is down, so need magnetic force up. By RHR, B must be into page

21. Motion of Q in uniform B field Force is perpendicular to B,v –B does no work! (W=F d cos  ) –Speed is constant (W=  K.E.  ) –Circular motion x x x x x x x Uniform B into page v F v F v F v F v F v F Force is perpendicular to B,v Solve for R: R 41

22. Motion of Q in uniform B field Force is perpendicular to B,v –B does no work! (W=F d cos  ) –Speed is constant (W=  K.E.  ) –Circular motion x x x x x x x Uniform B into page v F v F v F v F v F v F Force is perpendicular to B,v Solve for R: R 41

23. Preflight 8.6 What is the speed of the particle when it leaves chamber 2? 1) v 2 < v 1 2) v 2 = v 1 3) v 2 > v 1 1 2 v = 75 m/s q = +25 mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v 1 = 75 m/s up, and follows the dashed trajectory. 17% 46% 36% 43 Magnetic force is always perpendicular to velocity, so it changes direction, not speed of particle.

24. Preflight 8.8 Compare the magnitude of the magnetic field in chambers 1 and 2 1) B 1 > B 2 2) B 1 = B 2. 3) B 1 < B 2 1 2 v = 75 m/s q = +25 mC 37% 38% 26% Larger B, greater force, smaller R 45 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v 1 = 75 m/s up, and follows the dashed trajectory.

25. ACT A second particle with mass 2m enters the chamber and follows the same path as the particle with mass m and charge q=25 mC. What is its charge? 1) Q = 12.5 mC 2) Q = 25 mC 3) Q = 50 mC 1 2 v = 75 m/s q = ?? mC 48 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v 1 = 75 m/s up, and follows the dashed trajectory.

26. extra questions to try 1.Which angle do you use to determine the magnitude of the force on the charged particle? (  1,  2, either one). 2.Below I have drawn the trajectory for two charged particles traveling through a magnetic field. Is particle 1 positive or negatively charged? 3.If particles 1 and 2 have the same mass and velocity, which has the largest charge? B V 11 22 x x x x x x x 1 2 Either one sin(  ) = sin(180-  ) Positive Particle 1

27. Summary 50 We learned about magnetic fields B We learned about magnetic forces on moving charged particles