Download Current and Magnetic Field

Current and Magnetic Field
So far we have seen that when
a moving charge
or
current in a conductor
is exposed to a uniform magnetic field, it experiences a force.
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Lightning Revisited
Lightning bolts
carry ~200 C of
charge.
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Current and Magnetic Field
So far we have seen that when a moving charge or current in a
conductor is exposed to a uniform magnetic field, it experiences a
force.
We have also seen that when
a current loop is exposed to a magnetic field,
it experiences a torque.
This torque can be expressed in the general form:
= x
B
where
=I A
is the magnetic moment
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Magnetic Moment
The magnetic moment is a vector whose direction is obtained from
the direction of the current, using the right hand rule:
=I A
I
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Magnetic Moment
The magnetic moment is a
vector whose direction is
obtained from the direction of
the current, using the right
hand rule:
I
I
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Magnetic Moment on a current “coil”
A coil is a loop with more than one turn
In this case, each turn feels the torque for one loop
If there are N turns, the torque will multiply N fold.
= N I Ax
B
If we still write
=
xB
Then the magnetic
moment of the coil is:
= N I A
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Example 22.5 : Torque on a current “coil”
Dimensions 5.4cm x 8.5 cm
N = 25 turns
I = 15 mA
B =0.35 T parallel to the plane of the loop.
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Biot Savart Law: Magnetic field due
to an electric current
Question: what is the origin of the magnetic field ?
Observation of Biot and Savart: A current carrying conductor
gives rise to a magnetic field around it.
You have done the same experiment in your last lab.
d
B=k m
Id s x r
r
observation point P
2
r
I
d s
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Electric field due to an
electric charge
An analogous question to : what is the origin of the electric
field ?
dq
d E=k e 2
r
1 1
k e=
4 0
epsilon-zero is the “permittivity of free
space”
9
Biot Savart Law: Magnetic field due
to an electric current
Question: what is the origin of the magnetic field ?
Observation of Biot and Savart: A current carrying conductor
gives rise to a magnetic field around it.
You have done the same experiment in your last lab.
d
B=k m
Id s x r
r
2
0
k m=10 T.m/ A=
4
7
mu-zero is the
“permeability of free
space”
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Biot Savart Law: Magnetic field due
to an electric current
Simplify: consider the magnetic field at an axial point above a
current loop.
d
B=k m
Id s x r
r
I
0 I d s
dB=
4 x2
R2
2
P
r
x
R
r
d s
do in class
11
Biot Savart Law: Magnetic field due
to an electric current
Simplify: an infinite conductor
d
B=k m
Id s x r
r
observation point P
2
r
I
r
d s
do in class
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