1 / 37

Lectures 14-15 (Ch. 28) Sources of Magnetic Field

Lectures 14-15 (Ch. 28) Sources of Magnetic Field. 1 . B of a moving charge 2. Bio-Savarat law 3. Superposition principle 4. Force between two currents 5. Flux of B 6. Amper’s Law 7. Bohr’s magneton 8. 4 types of magnetic materials. B of a moving charge.

elinor
Download Presentation

Lectures 14-15 (Ch. 28) Sources of Magnetic Field

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lectures 14-15 (Ch. 28)Sources of Magnetic Field 1. B of a moving charge 2. Bio-Savarat law 3. Superposition principle 4. Force between two currents 5. Flux of B 6. Amper’s Law 7. Bohr’s magneton 8. 4 types of magnetic materials

  2. B of a moving charge

  3. Compare electric and magnetic forces

  4. Biot & Savart law (B of a segment of a current)

  5. B of a loop of a current

  6. Electromagnet(magnetic coil or solenoid) N loops of the current) For closely spaced loops (each loop at the same distance to observation point) of the same radius: In the center of the coil (x=0) N times stronger than from 1 loop Most of magnets used in industry are electromagnets. Attraction is due to magnetization of iron items. (see the end of the previous lecture)

  7. B of a stright wire Long wire: a>>x

  8. Oersted’s experiments and Oersted’s RH rule 1820: current produces B Hans Christian Ørsted (Oersted) (1777 – 1851)

  9. Superposition principle

  10. Examples. Find B at point P.

  11. A force between two currents NB: currents in the same direction attract each other. Currents in the opposite directions repeal each other. It’s different from charges of the same or opposite signs!

  12. Example. Magnetic bottle again (see also lecture 12) Now we understand also the structure of magnetic field between as a result of superposition of two fields produced by two coils. NB: rotation direction of a positive charge is opposite to the current in the coils. Repulsive interaction of opposite currents results in trapping the charged particles in the bottle.

  13. Example. Find the force acting on each piece of a rectangular conductor and the net force acting on the rectangular conductor.

  14. Flux of B Gauss’s law for E: Gauss’s law for B: Magnetic lines are closed lines. There are no magnetic carges.

  15. Example: Find a circulation of B produced by a current in the long straight wire for suggested integration passes and circulation directions. Circulation of B

  16. Arbitrary shape of the closed line

  17. Amper’s law Example. Find a circulation. Amper’s law allows one to find B for symmetric configurations of current.

  18. Conducting cylinder

  19. Coaxial cable Self-shielding

  20. Example. An infinite current sheet. There are n conductors per unite length. Each of them carries a current, I. Find B.

  21. B1 Example. Prove that if in the absence of currents B is unidirectional it has to be uniform. B2

  22. Solenoid (N loops) L’ L In the long solenoid (L>>a) B at the exit =(1/2) B in the center

  23. Toroidal solenoid (toroid)

  24. Example. Find a) the net force on the loop and b)the flux of B through the front surface of the loop. a I 2I L b d

  25. Bohr’s magneton Planck’s constant Bohr’s magneton e Different symmetries of e destributions S-state(L=0,μL=0) 1e:S≠0,μs ≠ 0 2e:Stotal=0, μs=0 P-state:L= μL ≠ 0

  26. 4 types of magnetic materials 1.Paramagnetics:μi≠0, Under the action of B0 alignment of μi struggles with chaotic thermal motion, resulting in Curie’s law Inside the material: Magnetic susceptibility Relative magnetic permeability

  27. 2. Ferromagnetics μi≠0, M ≠0 in domains

  28. Electromagnets typically contain a ferromagnetic core In the absence of an iron core: In the presence of an iron core: Magnetic permeability Narrow hysteresis loop, Often use superconducting wires

  29. Both paramagnetics and ferromagnetics are attracted to the magnet 1. Alignment (randomly oriented μ or M become parallel to B, i.e. material becomes magnetized ) B S N 2. Attraction(opposite poles attract each other) S N S N B

  30. Diamagnetics In the absence of magnetic field μi=0,M=0 In the presence of magnetic field M is induced in the direction opposite to external magnetic field (consequence of Lens’s low, see next lecture) These materials a repelled by magnets, though this repulsion is very week. 1. Induced M is anti- parallel to B0 B0 S N 2. Repulsion(similar poles repel each other) S N N S B0

  31. Meisner’s effect Superconductors (R=0) Perfect diamagnetics: Km=0, No magnetic field inside of superconductors

More Related