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The Compass

The Compass. 1088 Dream Poe Essays – Shen Kuo. 1. Permanent magnets. - Permanent magnets are dipoles (magnetic monopoles do not exist!) - The north and the south pole of a bar magnet have equal strength

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The Compass

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  1. The Compass 1088 Dream Poe Essays – ShenKuo 1

  2. Permanent magnets • - Permanent magnets are dipoles (magnetic monopoles do not exist!) • - The north and the south pole of a bar magnet have equal strength • - Two north poles or two south poles repel each other, a north pole and a south pole attract each other • - Magnetic field lines are directed from the north pole to the south pole H p F 2

  3. Torque on a magnet in a magnetic field A magnet (dipole) does not move in an uniform magnetic field, it only rotates 3

  4. Magnetic field from a current carrying wire p The magnetic pole strength is defined by considering the work done by the field in moving a pole once around the wire: I F The magnetic pole strength isdefined as work done per unit current. Thus, [p] = J/A = weber = Wb 4

  5. Ampère’s law 5

  6. Ampère’s law Ampère’s law can be used for structures with high symmetry 6

  7. Magnetic field due to current in small element Last week: dE dH + + + + + + + + + + + Electric charges at rest produce an electric field, moving electric charges produce an electric field and a magnetic field 7

  8. Magnetic field due to current in small element For an infinite long wire: dH Biot-Savart law Compare: 8

  9. Biot-Savart law for a closed circuit dl f 9

  10. Magnetic flux and magnetic flux density Magnetic flux: - B is a field density (number of lines per area) - M is an indication of total field through an area (number of field lines) - The unit of B is Wb/m2 = Tesla (T) 10

  11. Gauss’ law for magnetostatics The magnetic flux through any closed surface in a magnetic field is equal to the algebraic sum of the magnetic poles within the surface: Magnetic monopoles do not exist! 11

  12. Two sources of magnetic field Biot-Savart law Current through element dl: Single magnetic pole: Relations can be used to calculate the force between permanent magnets and current carrying objects (moving electric charges): 12

  13. Example 1 Force between two bar magnets: 13

  14. Example 2 Force from current in element dl on magnetic pole p: dl Force from magnetic pole p on current in element dl: dl redefinition of r r 14

  15. Example 3 Force from magnetic field on current loop: l Torque: F Magnetic dipole moment of a planar loop w F 15

  16. Electromotor 16

  17. From current to charge Magnetic field due to current (Biot-Savart): Magnetic field due to moving charge: Force on a current carrying wire: Force on an electric charge: 17

  18. CERN How big should the magnetic field be to steer the particles in a circular accelerator? Circumference of Large Hadron Collider (LHC): 27 km (R = 4.3 km) ac is centripetal acceleration (= v2/R) Actual dipole field at LHC: B = 8.4 T 18

  19. Force on a charge in E + B field - An electric charge accelerates in an electric field (gains kinetic energy). - An electric charge does not gain kinetic energy in a magnetic field. It is deflected in a direction perpendicular to v and B. 19

  20. B-field and E-field due to moving charges Magnetic field due to moving charge: Electric field due to an electric charge: +q 20

  21. Ferroelectric materials • - In ferroelectric materials the positive and negative ions are positioned in an off-centrosymmetric configuration • - Ferroelectric materials exhibit a spontaneous ferroelectric polarization 21

  22. Dielectric materials • - Dielectric materials are insulating materials • - Dielectric materials do not exhibit a spontaneous polarization, but a polarization is induced in an applied electric field • - The polarization results from a small displacement of the electronic charges with respect to the positive nucleus. 22

  23. Ferromagnetic materials - Ferromagnetism originates from electron spins and orbital moments - Each atom in a ferromagnetic material possesses a magnetic moment - Atomic moment interact with each other via direct exchange and dipolar interactions 23

  24. Ferromagnet Paramagnet Antiferromagnet T < TC T > TC 24

  25. Ferromagnetic materials 25

  26. Diamagnetic materials - In diamagnetic materials, current loops are induced by an external magnetic field - The field that they produce is opposite to the external magnetic field 26

  27. Reading @home • Chapter 16 • sebastiaan.van.dijken@aalto.fi 27

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