MAGNETOSTATICS Magnetic Fields Fundamental Postulates of Magnetostatics in Free Space.
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Transcript of MAGNETOSTATICS Magnetic Fields Fundamental Postulates of Magnetostatics in Free Space.
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MAGNETOSTATICS
Magnetic Fields
Fundamental Postulates of Magnetostatics in Free Space
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Magnetic Fields
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Magnetism and electricity have not been considered distinct phenomena until Hans Christian Oersted conducted an experiment that showed a compass deflecting in proximity to a current carrying wire
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Produced by-time varying electric fields
-permanent magnet (arises from quantum mechanical electron spin/ can be considered charge in motion=current )
-steady electric currents
m
AH SI
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If we place a wire with current I in the presence of a magnetic field, the charges in the conductor experience another force Fm
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Fm ~ q, u, B
q –chargeu –velocity vectorB -strength of the field (magnetic flux density)μr –relative permeabilityμ –absolute permeabilityμ0-permeability of the free spaceM=χmH- is the magnetization for linear andhomogeneous medium
BH1
)(104 70 H
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Relative permeabilities for a variety of materials
Material μ/(H m-1) μr Application
Ferrite U 60 1.00E-05 8 UHF chokes
Ferrite M33 9.42E-04 750 Resonant circuit RM cores
Nickel (99% pure) 7.54E-04 600 -
Ferrite N41 3.77E-03 3000 Power circuits
Iron (99.8% pure) 6.28E-03 5000 -
Ferrite T38 1.26E-02 10000 Broadband transformers
Silicon GO steel 5.03E-02 40000 Dynamos, mains transformers
supermalloy 1.26 1000000 Recording heads
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BuqF
EqF
m
e
FFF me
)( BuEqF
Lorentz’s Force equation
Note: Magnetic force is zero for q moving in the direction of the magnetic field (sin0=0)
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When electric current is passed through a magnetic field a force is exerted on the wire normal to both the magnetic field and the current direction. This force is actually acting on the individual charges moving in the conductor.
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nmm aFrFr sin
The magnetic force is exerting a torque on the current carrying coil
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Cross product
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Fundamental Postulates of Magnetostatics in
Free Space
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JB
B
0
0
0 J
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0s
sdB
Law of conservation of magnetic flux
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There are no magnetic flow sources, and the magnetic flux lines always close upon themselves
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Ampere’s circuital law
c
ss
IldB
sdJsdB
0
0
The circulation of the magnetic flux density in free space around any closed path is equal to μ0 times the total current flowing through the surface bounded by the path
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Stoke’s Theorem
cs
ldHsdH
Note: For a closed surface there will be no surface bounding external contour
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s
ldH
H c
s
0
lim
Proof: Sum over
where
nj asH
Note: The net contribution of all the common parts in the interior to the total line integral is 0 and only the contribution from the external contour C remains after summation
c
N
j cs
ldHldHj 1
0lim
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cs
ldHdsH
c
ldHJds
The maximum circulation of H per unit area as the areashrinks to zero is equal to the current density through that area
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Two possible Amperian paths around an infinite length line of current.
c
encIldH
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Differential Form Integral Form
Postulates of Magnetostatics
in Free Space
JB
B
0
0
c
s
IldB
sdB
0
0