1. A current carrying loop has a tendency to twist in magnetic field Compass needle: collection of atomic current loops Magnetic Torque on a Magnetic Dipole Moment

2. Torque (  ) = distance from the axle (lever arm) times perpendicular component of the force. Works with loops of any shape! Magnetic Torque: Quantitative Analysis

3. Calculate amount of work needed to rotate from angle  I to  f : Potential energy for a magnetic dipole moment Magnetic Dipole Moment: Potential Energy We chose “0” of potential energy in such as way that

4. Clicker Question Y Z X Direction of B I A)+Z B)-Z C)+Y D)-Y E)None of above

5. Potential energy for a magnetic dipole moment U= min -µB 0max µB 0 What is the energy difference between the highest and the lowest state? Picture of the U and µ in magnetic field – important in atomic and nuclear physics. Magnetic Dipole Moment: Potential Energy

6. B B Electric Motors

7. Tangential speed: Force on charges: Electric Generators

8. AC generator Electric Generators

9. Power Required to Turn a Generator

10. Imaging a hand cranked electrical generator How brightness of the lamp will depend on the speed at which generator is cranked: A.lamp will be brighter at low speed B.lamp will be brighter a high speed C.Lamp brightness will not depend on the speed at which generator is cranked

11. far from coil:far from dipole: magnetic dipole moment:  - vector in the direction of B Magnetic Dipole Moment

12. There is no force if field is uniform! Force on a Magnetic Dipole x Force exerted on dipole by magnetic field

13. Two magnets Force on a Magnetic Dipole

14. What is the distance at which one magnet can pick up another? =mg  0.1 N Exercise

15. charged tape Any magnetic field? Reference Frame

16. Two protons +e r 1 2 v v Electric force: E1E1 F 21,e Magnetic field: B1B1 Magnetic force: F 21,m Magnetic Forces in Moving Reference Frames

17. Electric force: Magnetic force: +e r 1 2 v v E1E1 F 21,e B1B1 F 21,m Ratio: (m/s) 2 =c 2 it is not accidental! Magnetic Forces in Moving Reference Frames

18. +e r 1 2 v v E1E1 F 21,e B1B1 F 21,m For v<<c the magnetic force is much smaller than electric force Full Lorentz force: Magnetic Forces in Moving Reference Frames downward

19. +e r 1 2 v v E1E1 F 21,e B1B1 F 21,m Who will see protons hit floor and ceiling first? 20 ns 15 ns Magnetic Forces in Moving Reference Frames