Magnetism

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Magnetism

• INEL 4151
• Dr. Sandra Cruz-Pol
• Electrical and Computer Engineering Dept.
• UPRM ch 7

http//www.treehugger.com/files/2008/10/spintronic
s-discover-could-lead-to-magnetic-batteries.php
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Applications
Motors Transformers MRI More
http//videos.howstuffworks.com/hsw/18034-electric
ity-and-magnetism-magnetic-levitation-video.htm
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H magnetic field intensity A/m B magnetic
field (or flux) density Teslas In free space
the permeability is
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Magnetic FieldBiot-Savart Law

• States that

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Example Segment of current
af
For an infinite line filament with current I
(a1180o and a20o)
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PE. 7.1 Find H at (0,0,5)
z

• Due to 10A current in
• where a290o and

(0,0,5)
r
b
1 y
10A
1
a1
x
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Ej. Find H at the origin for
y
1
a2
6A
r
af
1
x
a1
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Circular loop of I

• Defined by
• Apply Biot-Savart
• Only z-component of H survives due to symmetry

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Amperes Law

• Simpler
• Analogous to Gauss Law for Coulombs
• For symmetrical current distributions

Recall
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Amperes Law
We define an Amperian path where H is constant.
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Infinitely long coaxial cable
z
Four cases 1) For rlta
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Infinitely long coaxial cable
z
Four cases 2) For altrltb
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Infinitely long coaxial cable
Four cases 3) For bltrltbc
z
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Infinitely long coaxial cable
Four cases 4) For rgtbc
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Sheet of current distribution
Cross section is a Line!
Recall we had rv, rs in C/m3, C/m2
The H field is given by
The H field on the Amperian path is given by
In General
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PE. 7.5 Sheet of current

• Plane y 1 carries a current K50 az mA/m.
• Find H at (0,0,0).

y
K 50 mA/m
z
-x
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Infinite Line
Line Segment
Loop
Infinite Plane
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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

Webers Teslas m2
Recall
Monopole doesnt exist.
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Maxwells Equations for Static Fields
Differential form Integral Form
Gausss Law for E field.
Gausss Law for H field. Nonexistence of monopole
Faradays Law E field is conserved.
Amperes Law
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Magnetic Scalar and Vector Potentials, Vm A

• When J0, 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

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The magnetic vector potential, A, is defined
from
It can be shown that
(we used this)
The magnetic vector potential A is used in
antenna theory.
Substituting into equation for Magnetic Flux
This is another way of finding magnetic flux.
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P.E. 7.7 A current distribution causes a magnetic
vector potential of

• Find
• B at (-1,2,5)
• Answer
• Flux thru surface z1, 0 x 1, -1y 4
• Answer

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7.28
B (-6xz4x2y3xz2)ax(y6yz-4xy2)
ay(y2-z3-2x2-z)az Wb/m2 Draw surface
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Questions?
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El Descubrimiento de Ondas Gravitacionales

• El Pasado 11 de febrero de 2016 el Observatorio
  LIGO (Laser Interferometer Gravitational wave
  Observatory) anunció al mundo que había detectado
  la onda gravitacional generada por la fusión de
  dos agujeros negros.  
• Charla jueves 25 de febrero _at_1030 am _at_n Anf.
  Enfermería.