1. Chapter 25 Magnetism

2. Magnets 2 Magnets: interact on iron objects / other magnets 1) North pole (N-pole) & south pole (S-pole) 2) Opposite poles attract, like poles repel 3) Magnetic monopoles have not been found

3. Magnetic field 3 Magnets interact each other by magnetic field Magnetsmagnetic field create interact on magnetic field lines

4. Currents produce magnetism 4 H. C. Oersted found in 1820: An electric current produces a magnetic field. I A. M. Ampère: magnet ←→ magnet magnet ←→ current current ←→ current Magnetism is produced by electric currents. (molecular currents)

5. Nature of magnetism 5 A. Einstein: electromagnetic field in relativity Magnetism is the interaction of electric currents or moving charges. Magnetic field: 1) Created by / interacts on currents or moving charges 2) Closed field lines without beginning or end

6. Force on a current 6 Magnetic field exerts a force on a current (wire) It’s called Ampère force 1) Uniform field: I, l 

7. Definition of B 7 Define magnetic field by using: SI unit for B : Tesla (T), 1 T = 1 N/A·m =10 4 G 2) General case: nonuniform B & curved wire where is a differential length of the wire integral over the current-carrying wire

8. F on curved wire 8 Solution: Total magnetic force: It is equivalent to a straight wire from A to B Example1: Uniform magnetic field. Show that any curved wire connecting points A and B is exerted by the same magnetic force.

9. 9 Discussion: 1) It is valid only if B is uniform 2) Total force exerted on a current loop (coil)? 3) R B a b o I.

10. Nonuniform field 10 Solution: Total force on I 2 Example2: I 1 and I 2 are on the same plane. What is the force on I 2, if the magnetic field created by I 1 is I1I1 I2I2 ab dl direction? dr r

11. Interaction of currents 11 Question: Infinitely long current I 1 and circular current I 2 are insulated and on the same plane. What is the force between them? I1I1 I2I2 R I 2 dl

12. *Railgun 12 Weapon for space war in future → railgun High power ~ 10 7 J High velocity ~ 10 MachBattery & rail

13. Torque on a current loop (1) 13 Rectangular current loop in a uniform field

14. Torque on a current loop (2) 14 Torque on the loop: Magnetic dipole moment: where the direction is defined by right-hand rule compare with

15. Magnetic dipoles 15 These are valid for any plane current loop A small circular current → a magnetic dipole 1)  =  /2: maximum torque 2)  =0 or  : stable / unstable equilibrium 3) N loops coil / solenoid:

16. Magnetic moment of atom 16 Solution: Example3: Show that μ of an electron inside a hydrogen atom is related to the orbital momentum L of the electron by μ = eL/(2m). Orbital (angular) momentum: Classic / quantum model

17. μ of rotating charge 17 Solution: Magnetic moment Example4: A uniformly charged disk is rotating about the center axis (σ, R, ω). Determine the magnetic moment.. Rotating charge: Total magnetic moment: direction?

18. Force on moving charges 18 Magnetic field exerts a force on a moving charge: → Lorentz force 1) Magnitude: 2) Direction: right-hand rule, sign of q 3) Lorentz force doesn’t do work on the charge! If q < 0, has an opposite direction to

19. Motion in a uniform field (1) 19 1) : Free motion 2) :Uniform circular motion Point charge moves in a uniform magnetic field

20. Motion in a uniform field (2) 20 3) General case: Free motion + uniform circular motion Combination: the charge moves in a helix

21. Aurora & magnetic confinement 21 Aurora: Caused by high-energy charges Magnetic confinement: coil plasma “magnetic mirror”

22. Lorentz equation 22 Example5: A proton moves under both magnetic and electric field. Determine the components of the total force on the proton. (All in SI units) Solution: Total force

23. Different regions 23 Example6: A proton moving in a field-free region abruptly enters an uniform magnetic field as the figure. (a) At what angle does it leave ? (b) At what distance x does it exit from the field? Solution: Circular motion (a) (b)

24. Challenging question 24 Question: A electron is released from rest. If the field is shown as the figure, how does the electron move under the field? What is the path? - The path is a cycloid

25. The Hall effect 25 Current-carrying conductor / semiconductor placed in a magnetic field → Hall voltage Lorentz force → Hall field → equilibrium I H → Hall current

26. Applications of Hall effect 26 1) Distinguish the semiconductors 2) Measure magnetic field 3) Measure the carrier concentration Hall sensor / switch