ENTC 3331 RF Fundamentals. Dr. Hugh Blanton ENTC 3331. Magnetostatics . Magnetism Chinese—100 BC Arabs—1200 AD Magnetite—Fe 3 O 4 Found near Magnesia (now Turkey) Permanent magnet Not fundamental to magnetostatics. A permanent magnet is equivalent to a polar material in electrostatics.
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Chinese—100 BC
Arabs—1200 AD
Magnetite—Fe3O4
Found near Magnesia (now Turkey)
Permanent magnet
Not fundamental to magnetostatics.
A permanent magnet is equivalent to a polar material in electrostatics.
Equivalent to electrostatics
The theoretical structure of magnetostatics is very similar to electrostatics.
But there is one important empirical fact that accounts for all the differences between the theory of magnetostatics and electrostatics.
There is no magnetic monopole!
MagnetostaticsDr. Blanton  ENTC 3331  Magnetostatics 3
+
N
+
S
N
S
S
+
N
A magnetic monopole does not exist—A magnetostatic field has no sources or sinks!
+
Dr. Blanton  ENTC 3331  Magnetostatics 4
D s
u
rv
D l
Dr. Blanton  ENTC 3331  Magnetostatics 6
volume
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projection of onto the surface normal
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Conducting MediaDr. Blanton  ENTC 3331  Magnetostatics 11
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constant of proportionality (mobility)
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cylindrical shape.
A2
A1
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The reciprocal of conductivity Resistivity (ohms/meter).
Do not confuse charge distribution!
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JeanBaptiste Biot & Felix Savart developed the quantitative description for the magnetic field.
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field comes out of plane due to the cross product description for the magnetic field.
point of interest
differential section of conductor
contributes to field at
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magnetic field strength
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useful relationship
BiotSavart Law
Dr. Blanton  ENTC 3331  Magnetostatics 27
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X stationary current?
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Dr. Blanton  ENTC 3331  Magnetostatics 29
X stationary current?
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
righthanded rule
Dr. Blanton  ENTC 3331  Magnetostatics 30
X stationary current?
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
righthanded rule
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closed loop = 0
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X stationary current?
Examplez
BiotSavart Law
x
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X stationary current?
z
x
at P(x,z), points into the plane
Note that for a small dq, R is approximately unchanged when separated by dq which implies:
Dr. Blanton  ENTC 3331  Magnetostatics 35
X stationary current?
z
x
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z
y
field by I1 at location of I2
x
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z the current,
y
x
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the current,
Maxwell’s Magnetostatic EquationsCharge is the source of the electrostatic field
No equivalent in magnetostatics
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X rotational field.
line differential
field vector of the magnetostatic field
surface
current flowing through the surface
contour
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zaxis
z
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z
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Dr. Blanton  ENTC 3331  magnetostatic field is given byMagnetostatics 56
y
0.25m
0.25m
x
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Dr. Blanton  ENTC 3331  integralMagnetostatics 58
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0.25m
0.25m
x
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Dr. Blanton  ENTC 3331  theorem thatMagnetostatics 61
Dr. Blanton  ENTC 3331  theorem thatMagnetostatics 62
Dr. Blanton  ENTC 3331  theorem thatMagnetostatics 63