1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 14: June 22 nd 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Magnetism in Matter We now know how to build “electromagnets” (using electric current through a wire). We also found that a simple current loop produces a magnetic field / has a magnetic dipole moment. How about the “current” produced by an electron running around a nucleus? Let’s use a classical model (electron is a point charge orbiting around a positively charged nucleus. - + direction of motion of electron The tiny current loop produces a magnetic moment Orbital angular momentum of electron

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Magnetism in Matter - + L = “orbital angular momentum”

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Quantization

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Spin

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 Diamagnetism + magnetic moments cancel each other

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Diamagnetism + Net magnetic moment exists in the direction OPPOSITE to the magnetic field.

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Paramagnetism

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Ferromagnetism

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Faraday’s Law of Induction

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Example A circular loop of wire with radius r=5.0cm is in a magnetic field as shown. The Area vector of the loop is pointing in the x-direction. The magnetic field is: The magnetic field is turned off at a constant rate over a 5 second period. Calculate The induced emf in the loop. Voltmeter

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Example

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 Example a b A loop of material in a magnetic field is turned over as shown. The turn takes 0.50 s. The resistance of the wire loop is 0.2 . Calculate the induced current during this event. Assume that the loop is turned over at constant angular speed. The loop has width a=2.0cm and height b=4.0cm. B=1.0T.

14. Physics for Scientists and Engineers II, Summer Semester 2009 14 Example

15. Physics for Scientists and Engineers II, Summer Semester 2009 15 Motional emf - - ++

16. Physics for Scientists and Engineers II, Summer Semester 2009 16 Motional emf - - ++ R

17. Physics for Scientists and Engineers II, Summer Semester 2009 17 Motional emf R

18. Physics for Scientists and Engineers II, Summer Semester 2009 18 Motional emf

19. Physics for Scientists and Engineers II, Summer Semester 2009 19 Force required to pull the bar (no free lunch!) R

20. Physics for Scientists and Engineers II, Summer Semester 2009 20 Power comparison