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Exploring Magnetism: Applications and Fundamentals

Learn about magnetism, its applications in motors, transformers, MRI, and more. Understand magnetic field intensity, density, Biot-Savart Law, Ampere's Law, and Maxwell's Equations for static fields. Discover how magnetic scalar and vector potentials are used in finding magnetic flux. Dive into the world of magnetism with this comprehensive guide.

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Exploring Magnetism: Applications and Fundamentals

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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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