1. Magnets PH 203 Professor Lee Carkner Lecture 26

2. Magnetic Materials   The moving charges in a magnet are spinning or orbiting electrons   Problem:  The most common and well-known examples of magnetism result from extremely complex physics

3. Dipolar Field

4. No Magnetic Monopoles

5. Like Repel, Opposites Attract

6. Dipoles   =  B sin  U = -  B cos    When aligned with the field the energy is –  B, at right angles to the field the energy is 0, when opposite the field the energy is +  B  Dipoles that are not aligned with the field will turn until they are

7. Spin Magnetic Dipole   We can write this as  s  =  B = (eh/4  m) = 9.27X10 -24 J/T   The electron can feel a torque and has magnetic potential energy just like a normal magnetic dipole

8. Orbital Magnetic Dipole   The orbital angular momentum is quantized   We can write the orbital magnetic dipole moment as  orb = -m l  B  where  B is again the Bohr magneton and m l is the orbital magnetic quantum number (0, 1, 2, 3 …)

9. Magnetic Energy   Like any magnetic dipole (e.g., a loop of current) U = -  B ext   where potential energy is minimum  Note that the total energy between parallel and anti-parallel spins is 2  B ext

10. Diamagnetism   Net orbital magnetic dipole moment is zero  Like a bunch of loops with half with clockwise and half with counterclockwise currents   Speeds up electrons one way, slows down electrons other way   Almost all materials are diamagnetic, but the net effect is usually very weak

11. Paramagnetism   But they are usually randomly aligned and so there is no net magnetic field   An external magnetic field will cause the atomic dipole moments to try to align  Thermal motions of the material try to randomize the atoms

12. Curie’s Law   For low temperatures M can be found from Curie’s Law M = C(B ext /T)  Where C is the Curie constant   Strong magnetic fields and low temperatures produce more paramagnetism

13. Ferromagnetism   Due to an effect called exchange coupling, the electron spins of nearby atoms align with each other   Appling an external magnetic field can cause these domains to permanently align

14. The Earth’s Magnetic Field  The Earth has a magnetic field produced by the dynamo effect   We can find the direction of the Earth’s magnetic field with a small bar magnet called a compass   The Earth’s “north magnetic pole” is really a the south pole of a magnet!

15. Earth as a Magnet

16. Jupiter’s Magnetosphere

17. Planets and Magnetism  A planet will have a magnetic field if:  It has a conducting liquid interior  It has a fast enough rotation   This interaction region is known as the magnetosphere 

18. Next Time  Final exam, Thursday, 9am

19. To step down 120 household current to 12 volts, we would need a transformer with a ratio of turns between the primary and secondary transformer of, A)1 to 1 B)10 to 1 C)12 to 1 D)100 to 1 E)120 to 1

20. What is the direction of the magnetic field in the PAL at a point due east of the center of the region? A)North B)South C)East D)West E)Up

21. Consider a standard 6-sided die. Suppose the magnetic flux through each side 1-5 is equal to the number of spots on the side (in Wb) and points outward for even sides and inward for odd. What is the flux magnitude through the side with 6 spots? A)1 Wb B)2 Wb C)3 Wb D)6 Wb E)9 Wb

22. Consider 3 Gaussian surfaces. (1) encloses the north pole of a bar magnet, (2) encloses the south pole of a bar magnet, and (3) encloses the entire bar magnet. Rank the surfaces according to the total magnetic flux through them, greatest first. A)1, 2, 3 B)3, 2, 1 C)2, 1, 3 D)1, 3, 2 E)All tie