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Biot-Savart LawBiot-Savart law:
The constant o is called the permeability of free space
o = 4 x 10-7 T. m / A
24oμ d
dπ r
s rB
ˆI
24oμ d
π r
s rB
ˆI
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for a Long, Straight ConductorThe thin, straight
wire is carrying a constant current
Integrating over all
the current elements
B
2
1
1 2
4
4
θo
θ
o
μB θ dθ
πaμ
θ θπa
I
cos
Isin sin
sin d dx θ s r k ˆˆ
2
IoμBπa
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for a Curved Wire SegmentFind the field at
point O due to the wire segment
I and R are constants
will be in radians
B
4
IoμB θπR
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for a Circular Loop of WireConsider the previous result, with a full circle
= 2
This is the field at the center of the loop
B
24 4 2o o oμ μ μ
B θ ππa πa a
I I I
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for a Circular Current LoopThe loop has a
radius of R and carries a steady current of I
Find the field at point P
B
2
32 2 22
ox
μ aB
a x
I
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Magnetic Force Between Two Parallel ConductorsTwo parallel wires
each carry a steady current
The field due to the current in wire 2 exerts a force on wire 1 of F1 = I1ℓ B2
1 21 2
I IoμFπa
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Ampere’s LawAmpere’s law states
that the line integral of around any closed
path equals oI where I is the total steady current passing through any surface bounded by the closed path:
s od μ B
I
dB s
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Magnetic Field of a ToroidFind the field at a
point at distance r from the center of the toroid
The toroid has N turns of wire
2
2
o
o
d B πr μ N
μ NB
πr
B s
( ) I
I
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Magnetic FluxThe magnetic flux
associated with a magnetic field is defined in a way similar to electric flux
The magnetic flux B is
The unit of magnetic flux is T.m2 = WbWb is a weber
B d B A
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Gauss’ Law in MagnetismGauss’ law in magnetism says the
magnetic flux through any closed surface is always zero:
0d B A
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Earth’s Magnetic FieldThe Earth’s south
magnetic pole is located near the north geographic pole
The Earth’s north magnetic pole is located near the south geographic pole