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Chapter 29
Magnetic Fields Due to Currents
In this chapter we will explore the relationship between an electric
current and the magnetic field it generates in the space around it. We
will follow a twoprong approach, depending on the symmetry of the
problem.
For problems with low symmetry we will use the
law of BiotSavart
in
combination with the principle of superposition.
For problems with high symmetry we will introduce
Ampere’s law
.
Both approaches will be used to explore the magnetic field generated by
currents in a variety of geometries (straight wire, wire loop, solenoid
coil, toroid coil)
We will also determine the force between two parallel current carrying
conductors.
We will then use this force to define the SI unit for electric
current (the Ampere)
(29 – 1)
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View Full Document Hans Christian Oersted
17771851
Oersted observed that a magnetic needle is
deflected from its normal northsouth
orientation in the presence of a wire that
carries an electric current. Thus he concluded
that an electric current produces in its vicinity
a magnetic field
.
This law gives the magnetic field
generated by a wire
segment of length
that carries a current
.
Consider
the geometry shown in the figure.
Associated with the
element
dB
ds
i
ds
The law of Biot Savart
G
we define a vector
that has
magnitude whch is equal to the length
. The direction
of
is the same as that of the current that flows through
segment .
ds
ds
ds
ds
G
G
A
3
The magnetic field
generated at point P by the element
located at point A
is given by the equation:
.
Here
is the vector that connects
4
point A (location of element
) w
o
dB
ds
i ds r
dB
r
r
ds
μ
π
×
=
G
G
GG
G
G
76
2
ith point P at which we want to determine
.
The constant
4
10 T m/A
1.26 10 T m/A
and is known as
sin
"
".
The magnitude of
is:
4
Here
is the angle
o
o
dB
i ds
dB
dB
r
μπ
θ
−−
=×
⋅
=
×
⋅
=
G
G
permeability constant
between
and
.
ds
r
3
4
o
i ds r
dB
r
×
=
G
(29 – 2)
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View Full Document Jean Baptiste Biot
17741862
The magnitude of the magnetic field
generated by the wire at point P
located at a distance
from the wire
is given by the equation:
2
o
i
B
R
R
μ
π
=
Magnetic field generated by a long
straight wire
2
o
i
B
R
=
The magnetic field lines form circles that have their centers
at the wire.
The magnetic field vector
is tangent to the
magnetic field lines.
The sense for
is given by the
.
We po
B
B
right
hand rule
G
G
int the thumb of the right hand in the
direction of the current.
The direction along which the
fingers of the right hand curl around the wire gives the
direction of
.
B
G
(29 – 3)
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View Full Document 2
Consider the wire element of length
shown in the figure.
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This document was uploaded on 11/04/2011 for the course PHY 108 at SUNY Buffalo.
 Fall '08
 IASHVILI
 Current

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