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Magnetism

Magnetism. INEL 4151 Dr. Sandra Cruz-Pol Electrical and Computer Engineering Dept. UPRM ch 7. http://www.treehugger.com/files/2008/10/spintronics-discover-could-lead-to-magnetic-batteries.php. http://videos.howstuffworks.com/hsw/11955-magnetism-introduction-to-magnetism-video.htm.

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Magnetism

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  1. Magnetism INEL 4151 Dr. Sandra Cruz-Pol Electrical and Computer Engineering Dept. UPRM ch 7 http://www.treehugger.com/files/2008/10/spintronics-discover-could-lead-to-magnetic-batteries.php

  2. http://videos.howstuffworks.com/hsw/11955-magnetism-introduction-to-magnetism-video.htmhttp://videos.howstuffworks.com/hsw/11955-magnetism-introduction-to-magnetism-video.htm

  3. Applications Motors Transformers MRI More… http://videos.howstuffworks.com/hsw/18034-electricity-and-magnetism-magnetic-levitation-video.htm

  4. H= magnetic field intensity [A/m] B= magnetic field density [Teslas] In free space the permeability is:

  5. Magnetic FieldBiot-Savart Law • States that:

  6. Example a2 af a1 r For an infinite line filament with current I (a1=180o and a2=0o):

  7. PE. 7.1 Find H at (0,0,5) z • Due to current in (figure): where a1=90o and (0,0,5) 1 y 10A 1 x

  8. z Circular loop dHz dHr • Defined by • Apply Biot-Savart: • Only z-component of H survives due to symmetry: R r y dl x

  9. Ampere’s Law • Simpler • Analogous to Gauss Law for Coulombs • For symmetrical current distributions

  10. Ampere’s Law We define an Amperian path where H is constant.

  11. Infinitely long coaxial cable z Four cases: 1) For r<a

  12. Infinitely long coaxial cable z Four cases: 2) For a<r<b

  13. Infinitely long coaxial cable Four cases: 3) For b<r<b+c z

  14. Infinitely long coaxial cable Four cases: 4) For r>b+c

  15. Sheet of current distribution z Cross section is a Line! 4 b The H field is given by: a 1 y 3 K [A/m] 2 The H field on the Amperian path is given by: x

  16. PE. 7.5 Sheet of current Plane y=1 carries a current K=50 az mA/m. Find H at (0,0,0). y K =50 mA/m z -x

  17. A toroid A circular ring-shaped magnetic core of iron powder, ferrite, or other material around which wire [N- loops] is coiled to make an inductor. Toroidal coils are used in a broad range of applications, such as high-frequency coils and transformers. Toroidal inductors can have higher Q factors and higher inductance than similarly constructed solenoid coils. This is due largely to the smaller number of turns required when the core provides a closed magnetic path. The magnetic flux in a toroid is largely confined to the core, preventing its energy from being absorbed by nearby objects, making toroidal cores essentially self-shielding. Fields stay inside core, no interference.

  18. Magnetic Flux Density, B • The magnetic flux is defined as: which flows through a surface S. • The total flux thru a closed surface in a magnetic field is: Monopole doesn’t exist.

  19. Maxwell’s Equations for Static Fields

  20. Magnetic Scalar and Vector Potentials, Vm & A When J=0, the curl of H is =0, then recalling the vector identity: • We can define a Magnetic Scalar Potential as: • The magnetic Vector Potential A is defined:

  21. The magnetic vector potential, A, is It can be shown that: The magnetic vector potential A is used in antenna theory. Substituting into equation for Magnetic Flux: This is another way of finding magnetic flux.

  22. P.E. 7.7 A current distribution causes a magnetic vector potential of: Find : • B at (-1,2,5) Answer: • Flux thru surface z=1, 0≤x≤1, -1≤y ≤4 Answer :

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