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1. http://www.lab-initio.com (nz138.jpg)

2. Today’s lecture is brought to you by… …the Right Hand Rule.

3. Announcements • Exam 2 is next week. Contact me by the end of today’s lecture if you have special circumstances different than for exam 1. • Exam 2 will cover chapters 4.3-7. But not today’s material.

4. Physics 24 Test Room Assignments, Spring 2014: Instructor Sections Room Dr. Hale F, H G-31 EECH Dr. Parris G, L 125 BCH Mr. Upshaw E, K 199 Toomey Mr. Viets A, C 104 Physics Dr. Vojta B, D G-3 Schrenk 4:30 & 5:30 Exams 202 Physics Special Needs Testing Center Exam is from 5:00-6:15 pm! Know the exam time! Find your room ahead of time! If at 5:00 on test day you are lost, go to 104 Physics and check the exam room schedule, then go to the appropriate room and take the exam there.

5. Today’s agenda: Review and some interesting consequences of F=qvxB. You must understand the similarities and differences between electric forces and magnetic forces on charged particles. Magnetic forces and torques on current loops. You must be able to calculate the torque and magnetic moment for a current-carrying wire in a uniform magnetic field. Magnetic Flux and Gauss’ Law for Magnetism. You must be able to calculate magnetic flux and recognize the consequences of Gauss’ Law for Magnetism. Applications: galvanometers, electric motors, rail guns. You must be able to use your understanding of magnetic forces and magnetic fields to describe how electromagnetic devices operate.

6. Reminder: signs Include the sign on q, properly account for the directions of any two of the vectors, and the direction of the third vector is calculated “automatically.” If you determine the direction “by hand,” use the magnitude of the charge. Everything in this equation is a magnitude. The sign of r had better be +!

7. y  z x z  y x Reminder: left- and right-hand axes This is a right-handed coordinate system: This is not: For the magnetism part of physics 24, you MUST use right-hand axes. And you’d better use your right hand when applying the right-hand rule!

8. y  z x z  y x Handy way to “see” if you have drawn right-hand axes: Z ? y x ? I personally find the three-fingered axis system to often (but not always) be the most useful way to apply the right-hand rule.

9. “In and does it matter which finger I use for what?”             You’ll learn about F = IL x B later in today’s lecture.             No, as long as you keep the right order. No, as long as you keep the right order. All three of these will work:

10.       This works: Switching only two is wrong! This doesn’t: “The right-hand rule is unfair! Physics is discriminating against left-handers!” No, you can get the same results with left-hand axes and left-hand rules. See thisweb page.

11. But Physics 24 does discriminate against left-handers! This is Captain Jack Crossproduct. He visits our classes occasionally (see the physics on the blackboard behind him). You don’t want to see what he does with his scimitar when he sees a left hand used for the right hand rule! The right hand rule is just a way of determining vector directions in a cross product without having to do math.

12. Magnetic and Electric Forces The electric force acts in the direction of the electric field. The electric force is nonzero even if v=0. The magnetic force acts perpendicular to the magnetic field. The magnetic force is zero if v=0.

13. + + Magnetic and Electric Forces The electric force does work in displacing a charged particle. E D F The magnetic force does no work in displacing a charged particle! v  B ds Amazing! F

14. Today’s agenda: Review and some interesting consequences of F=qvxB. You must understand the similarities and differences between electric forces and magnetic forces on charged particles. Magnetic forces and torques on current loops. You must be able to calculate the torque and magnetic moment for a current-carrying wire in a uniform magnetic field. Magnetic Flux and Gauss’ Law for Magnetism. You must be able to calculate magnetic flux and recognize the consequences of Gauss’ Law for Magnetism. Applications: galvanometers, electric motors, rail guns. You must be able to use your understanding of magnetic forces and magnetic fields to describe how electromagnetic devices operate.

15. Magnetic Forces and Torques on Current Loops We showed (not in general, but illustrated the technique) that the net force on a current loop in a uniform magnetic field is zero. No net force means no motion. No net force means no motion NOT. Example: a rectangular current loop of area A is placed in a uniform magnetic field. Calculate the torque on the loop. Let the loop carry a counterclockwise current I and have length L and width W. I L B The drawing is not meant to imply that the top and bottom parts are outside the magnetic field region. W

16. There is no force on the “horizontal” segments because the current and magnetic field are in the “same” direction. There is no force on the “horizontal” segments because the current and magnetic field are in the “same” direction. Homework hint (know why). FL FR   L B I The vertical segment on the left “feels” a force “out of the page.” W The vertical segment on the right “feels” a force “into the page.” The two forces have the same magnitude: FL = FR = ILB. Because FL and FR are in opposite directions, there is no net force on the current loop, but there is a net torque.

17. Top view of current loop, looking “down,” at the instant the magnetic field is parallel to the plane of the loop. FR B   IR IL In general, torque is FL area of loop = WL

18. FR When the magnetic field is not parallel to the plane of the loop…  IR B    IL A FL Define A to be a vector whose magnitude is the area of the loop and whose direction is given by the right hand rule (cross A into B to get ). Then

19. IA is defined to be the magnetic moment of the current loop. Magnetic Moment of a Current Loop FR  IR Alternative way to get direction of A: curl your fingers (right hand) around the loop in the direction of the current; thumb points in direction of A. B    IL A FL Homework Hint Your starting equation sheet has:

20. Energy of a magnetic dipole in a magnetic field You don’t realize it yet, but we have been talking about magnetic dipoles for the last 5 slides. A current loop, or any other body that experiences a magnetic torque as given above, is called a magnetic dipole. Energy of a magnetic dipole? You already know this: Today: Electric Dipole Magnetic Dipole Homework Hint

21. Example: a magnetic dipole of moment is in a uniform magnetic field . Under what conditions is the dipole’s potential energy zero? Minimum? Under what conditions is the magnitude of the torque on the dipole minimum? Maximum?

22. Today’s agenda: Review and some interesting consequences of F=qvxB. You must understand the similarities and differences between electric forces and magnetic forces on charged particles. Magnetic forces and torques on current loops. You must be able to calculate the torque and magnetic moment for a current-carrying wire in a uniform magnetic field. Magnetic Flux and Gauss’ Law for Magnetism. You must be able to calculate magnetic flux and recognize the consequences of Gauss’ Law for Magnetism. Applications: galvanometers, electric motors, rail guns. You must be able to use your understanding of magnetic forces and magnetic fields to describe how electromagnetic devices operate.

23. B Magnetic Flux and Gauss’ Law for Magnetism Magnetic Flux We have used magnetic field lines to visualize magnetic fields and indicate their strength. We are now going to count the number of magnetic field lines passing through a surface, and use this count to determine the magnetic field.

24. A B B  The magnetic flux passing through a surface is the number of magnetic field lines that pass through it. Because magnetic field lines are drawn arbitrarily, we quantify magnetic flux like this: M=BA. If the surface is tilted, fewer lines cut the surface. If these slides look familiar, refer back to lecture 4!

25. We define A to be a vector having a magnitude equal to the area of the surface, in a direction normal to the surface. Because A is perpendicular to the surface, the amount of A parallel to the electric field is Acos. A  B  The “amount of surface” perpendicular to the magnetic field is Acos. A = A cos  so M = BA = BA cos. Remember the dot product from Physics 23?

26. If the magnetic field is not uniform, or the surface is not flat… divide the surface into infinitesimal surface elements and add the flux through each… B dA your starting equation sheet has if possible, use

27. a surface integral, therefore a double integral If the surface is closed (completely encloses a volume)… …we count lines going out as positive and lines going in as negative… B dA But there are no magnetic monopoles in nature (jury is still out on 2009 experiments, but lack of recent developments suggests nothing to see). If there were more flux lines going out of than into the volume, there would be a magnetic monopole inside.

28. Therefore B Gauss’ Law for Magnetism! dA This law may require modification if the existence of magnetic monopoles is confirmed. Gauss’ Law for magnetism is not very useful in this course. The concept of magnetic flux is extremely useful, and will be used later!

29. You have now learned Gauss’s Law for both electricity and magnetism. These equations can also be written in differential form: Congratulations! You are ½ of the way to being qualified to wear…

30. The Missouri S&T Society of Physics Student T-Shirt! This will not be tested on the exam.

31. Today’s agenda: Review and some interesting consequences of F=qvxB. You must understand the similarities and differences between electric forces and magnetic forces on charged particles. Magnetic forces and torques on current loops. You must be able to calculate the torque and magnetic moment for a current-carrying wire in a uniform magnetic field. Magnetic Flux and Gauss’ Law for Magnetism. You must be able to calculate magnetic flux and recognize the consequences of Gauss’ Law for Magnetism. Applications: galvanometers, electric motors, rail guns. You must be able to use your understanding of magnetic forces and magnetic fields to describe how electromagnetic devices operate.

32. The Galvanometer Now you can understand how a galvanometer works… When a current is passed through a coil connected to a needle, the coil experiences a torque and deflects. See the link below for more details. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/galvan.html#c1

33. Electric Motors http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

34. Hyperphysics has nice interactive graphics showing how dc and ac motors work.

35. No lecture on magnetic forces would be complete without... …the rail gun! Current in the rails (perhaps millions of amps) gives rise to magnetic field (we will study this after exam 2). Projectile is a conductor making contact with both rails. Magnetic field of rails exerts force on current-carrying projectile. The 10 meter rail gun at the University of Texas.

36. Today’s lecture was brought to you by… …the Right Hand Rule.