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Magnetic Materials

Magnetic Materials. www.phy.iitb.ac.in/~ph102. Magnetic Material. Magnetic field in materials is due to tiny electric current loops or magnetic dipoles . At normal temperatures the magnetic moments of the dipoles are randomly oriented so that the net magnetic moment is zero.

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Magnetic Materials

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  1. Magnetic Materials www.phy.iitb.ac.in/~ph102

  2. Magnetic Material • Magnetic field in materials is due to tiny electric current loops or magnetic dipoles. At normal temperatures the magnetic moments of the dipoles are randomly oriented so that the net magnetic moment is zero. • Magnetization = Magnetic moment per unit volume • When an external magnetic field is applied the dipoles align and the material develops a magnetization.

  3. Dia-, Para-, and Ferronmagnetism • Electric dipoles always align in the direction of magnetic field but different magnetic material behave differently. • Diamagnetic material have their manetization direction opposite to that of B. • Paramagnetic material have M parallel to B • Ferromagnets are those which retain their magnetization even after the magnetic field is withdrawn – Hysteresis.

  4. Types of magnetic materials

  5. Paramagnetic material in Magnetic Field • Atomic magnets are oriented in direction of B, currents in adjacent loops cancel giving rise to a surface current

  6. Force on a magnetic dipole • Force on a current carrying loop is B L A

  7. z C B y O A x A current loop experiences a force in an inhomogeneous Field

  8. z C B y O A x Dipole in Inhomogeneous Magnetic Field

  9. Dipole in Inhomogeneous Magnetic Field • Assume that the derivatives are constant at the boundaries of small loops

  10. Torque on a current loop • A dipole experiences a torque in a constant magnetic field • Torque is zero when the magnetic moment is parallel to the field. To bring the dipole to a position which makes an angle q with the magnetic field, one has to do work.

  11. Field due to a magnetic dipole • For paramagnetic material, magnetization is proportional to the external field. • Magnetic field on the axis of a circular coil of radius a was seen to be

  12. Vector Potential of a current loop

  13. Vector Potential of a current loop z x P dA r q r a O x f dl y

  14. z x P dA r q r a O x f dl y dl’

  15. Vector Potential of a current loop

  16. Vector Potential of a current loop

  17. Vector Potential of magnetized substance • If M is the magnetization, a volume dt contains Mdt dipoles. The vector potential at a point P is given by

  18. Vector Potential of magnetized substance

  19. Bound currents

  20. t K Uniformly magnetized slab M

  21. Free and Bound Currents • Net current is due to actual transport of charges while bound current is due to magnetization. • Ampere’s Law for magnetized material contains contribution due to both types of current and is,

  22. Fields B, H and M • Define H-field by

  23. Example • An infinitely long cylinder of radius R contains a frozen in magnetization M=kr, where r is distance from axis and no free current. Find B, H, M.

  24. r L Infinitely long cylinder • Use Ampere’s Law. As the current is in f direction, field are along the axis. B is zero outside the cylinder.

  25. Magnetized cylinder (contd.)

  26. z q M R q Rsin q n A uniformly magnetized Cylinder

  27. z q M R q Rsin q n Uniformly magnetized sphere • From symmetrically located pairs of elements horizontal components cancel while vertical components add up.

  28. Example : Large Piece of uniformly magnetized material from which a sphere is scooped out. B0

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