1 / 21

Chapter-6 : Magnetic Fields in Matter

Chapter-6 : Magnetic Fields in Matter. Magnetization Dia-magnets, Paramagnets, Ferro-magnets At microscopic level, electrons in atom revolve around the nucleus as well have spin. This will form tiny current loop and hence dipole moment.

blossom-benjamin
Download Presentation

Chapter-6 : Magnetic Fields in Matter

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. Chapter-6 : Magnetic Fields in Matter • Magnetization • Dia-magnets, Paramagnets, Ferro-magnets • At microscopic level, electrons in atom revolve around the nucleus as well have spin. This will form tiny current loop and hence dipole moment. • Ordinarily the dipole moments in matter cancel each other due to random orientation of atoms. Dr. Rakesh Choubisa, BITS, Pilani

  2. What happens when a material is subjected to external magnetic field. • Unlike electric field, magnetic dipoles aligns either along field (para-magnetism) or opposite to it (Diamagnetism) . • Some materials retain magnetic property even after switching off the magnetic field (Ferromagnetism). Dr. Rakesh Choubisa, BITS, Pilani

  3. Torque & Force on Magnetic Dipoles Z Z m m F θ θ I Y θ Y θ b a F X Dr. Rakesh Choubisa, BITS, Pilani

  4. Torque & Force on Magnetic Dipoles • In a uniform magnetic field; net force is zero. • While in non-uniform magnetic field, it is non-zero and can be expressed as (Pr. 6.3); Similar to the electrostatics case. Dr. RakeshChoubisa, BITS, Pilani

  5. Pr. 6.1: Calculate the torque exerted on the square loop due to the circular loop. • Torque will be Dr. Rakesh Choubisa, BITS, Pilani

  6. Effect of a magnetic field on atomic orbit • Electrons in atom revolves around nucleus and contribute steady current of period T. Z B R v e- m Dr. Rakesh Choubisa, BITS, Pilani

  7. Effect of a magnetic field on atomic orbit • Electron will speed up by the amount; • Hence change in magnetic dipole; Dipole always aligns opposite to filed Dr. Rakesh Choubisa, BITS, Pilani

  8. Magnetization • In the presence of external magnetic field; • We have a net polarization either • Along the field (Para-magnetism related to spin of unpaired electrons) • Opposite to the field (Dia-magnetism related to the orbital motion of electrons) • For this we define magnetization as magnetic dipoles per unit volume. Dr. Rakesh Choubisa, BITS, Pilani

  9. The Field of a Magnetized Object rs m dΓ’ Dr. Rakesh Choubisa, BITS, Pilani

  10. The Field of a Magnetized Object • Using product rule 7, we have; Volume bound current Jb Surface bound current Kb Dr. RakeshChoubisa, BITS, Pilani

  11. Problem 6.8 A long cylinder of radius R carries a magnetizationFind the magnetic field. Dr. Rakesh Choubisa, BITS, Pilani

  12. Physical interpretation of bound currents • When we have uniform magnetization, we have, on average, surface bound current due to cancellation of currents of all the internal sides of tiny current loops within the material. • In a non-uniform magnetization, we have also volume bound current due to net current from the internal tiny current loops. • In both cases; current is due to motion of bound charges attached to each atom. Dr. Rakesh Choubisa, BITS, Pilani

  13. The Auxiliary Field H • Ampere’s law in Magnetized Materials: • Total current through the material is (bound + free currents); • Using Ampere’s differential law; Dr. Rakesh Choubisa, BITS, Pilani Dr. Rakesh Choubisa, BITS, Pilani

  14. The Auxiliary Field H • We get differential form of Ampere’s law for H • Also, we have the integral form; Dr. Rakesh Choubisa, BITS, Pilani

  15. Pr. 6.12: An infinite long cylinder, of radius R, carries a frozen-in magnetization, parallel to the axis, , and there is no free current anywhere. Find the magnetic field. • It can also be solved using H. Dr. Rakesh Choubisa, BITS, Pilani

  16. A Deceptive Parallel • H and B are not like even if we have similar from of Ampere’s law. • As field is found by both curl and div. of vector, div. of B is always zero however div. of H in general is not zero (as, div. M is not zero) & hence both are not like. • However, when Div. of M is zero, the parallel between B and µ0H is faithful. Dr. Rakesh Choubisa, BITS, Pilani

  17. Boundary Conditions Dr. RakeshChoubisa, BITS, Pilani

  18. Linear and Nonlinear Media • When field is weak enough, we should write; • But customary it is written in terms of H; Magnetic susceptibility Dr. Rakesh Choubisa, BITS, Pilani Dr. Rakesh Choubisa, BITS, Pilani

  19. Linear and Nonlinear Media • Materials which obey this relation is called linear media • Where; Permeability of the material Dr. Rakesh Choubisa, BITS, Pilani Dr. Rakesh Choubisa, BITS, Pilani

  20. Pr. 6.17: A current I flows down a long straight wire, made of linear material with susceptibility , of radius a. Find the magnetic field, all bound currents and the net bound current flowing down the wire. The current I is distributed uniformly. Dr. Rakesh Choubisa, BITS, Pilani

  21. Pr. 6.25: A toy consists of donut-shaped permanent magnet. (a) If you put two back-to-back magnets on the rod. At what height (z) does the upper one float?(b) If you now add a third magnet, write the equation of motion for the floating condition for the upper magnets. y z x Dr. Rakesh Choubisa, BITS, Pilani

More Related