Transcript Measuring the Strength of a Magnetic Field PowerPoint

Measuring the strength of a Magnetic
Field
© David Hoult 2009
When current flows through a conductor which is
in a magnetic field, it experiences a force, except
when the conductor is
© David Hoult 2009
When current flows through a conductor which is
in a magnetic field, it experiences a force, except
when the conductor is parallel to the flux lines
© David Hoult 2009
When current flows through a conductor which is
in a magnetic field, it experiences a force, except
when the conductor is parallel to the flux lines
The direction of the force is at 90° to both the
current and the flux lines
© David Hoult 2009
When current flows through a conductor which is
in a magnetic field, it experiences a force, except
when the conductor is parallel to the flux lines
The direction of the force is at 90° to both the
current and the flux lines
Fleming’s left hand rule helps to remember the
relation between the three directions…
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
Thumb
First finger
Second finger
© David Hoult 2009
ThuMb
Motion
First finger
Second finger
© David Hoult 2009
ThuMb
Motion
First finger
Field
Second finger
© David Hoult 2009
ThuMb
Motion
First finger
Field
SeCond finger
Current
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
Factors affecting the Magnitude of the Force
The force depends on
© David Hoult 2009
The force depends on
- the current flowing through the conductor, I
© David Hoult 2009
The force depends on
- the current flowing through the conductor
- the length of conductor in the field
© David Hoult 2009
The force depends on
- the current flowing through the conductor
- the length of conductor in the field
Experiments show that
© David Hoult 2009
The force depends on
- the current flowing through the conductor
- the length of conductor in the field
Experiments show that
F a current, I
© David Hoult 2009
The force depends on
- the current flowing through the conductor
- the length of conductor in the field
Experiments show that
F a current, I
F a length of conductor, L
© David Hoult 2009
The force depends on
- the current flowing through the conductor
- the length of conductor in the field
Experiments show that
F a current, I
F a length of conductor, L
F = I L × a constant
© David Hoult 2009
The force depends on
- the current flowing through the conductor
- the length of conductor in the field
Experiments show that
F a current, I
F a length of conductor, L
F = I L × a constant
magnetic field strength or
© David Hoult 2009
The force depends on
- the current flowing through the conductor
- the length of conductor in the field
Experiments show that
F a current, I
F a length of conductor, L
F = I L × a constant
magnetic field strength or magnetic flux density
© David Hoult 2009
F = ILB
© David Hoult 2009
F = ILB
units of B Newtons per Amp per meter, NA-1m-1
© David Hoult 2009
F = ILB
units of B Newtons per Amp per meter, NA-1m-1
1 NA-1m-1 is called 1 Tesla (1 T)
© David Hoult 2009
F = ILB
units of B Newtons per Amp per meter NA-1m-1
1 NA-1m-1 is called 1 Tesla (1 T)
The flux density of a magnetic field is
© David Hoult 2009
F = ILB
units of B Newtons per Amp per meter NA-1m-1
1 NA-1m-1 is called 1 Tesla (1 T)
The flux density of a magnetic field is the force per
unit current per unit length acting on a conductor
placed at 90° to the field
© David Hoult 2009
F = ILB
units of B Newtons per Amp per meter NA-1m-1
1 NA-1m-1 is called 1 Tesla (1 T)
The flux density of a magnetic field is the force per
unit current per unit length acting on a conductor
placed at 90° to the field
F = I L B sin q
© David Hoult 2009
Force acting on a charged particle
moving through a magnetic field
© David Hoult 2009
© David Hoult 2009
Consider a conductor of length L, having n free
electrons per unit volume. A current, I, is flowing
through it
© David Hoult 2009
Consider a conductor of length L, having n free
electrons per unit volume. A current, I, is flowing
through it
© David Hoult 2009
In this piece of conductor there are
© David Hoult 2009
In this piece of conductor there are NAL free
electrons
© David Hoult 2009
In this piece of conductor there are NAL free
electrons
If all these electrons pass through end x in time t
then the current, I is given by
© David Hoult 2009
In this piece of conductor there are NAL free
electrons
If all these electrons pass through end x in time t
then the current, I is given by
nALe
t
© David Hoult 2009
If there is a magnetic field of flux density B at 90°
to the current, the conductor will experience a
force of magnitude
© David Hoult 2009
If there is a magnetic field of flux density B at 90°
to the current, the conductor will experience a
force of magnitude I L B
© David Hoult 2009
If there is a magnetic field of flux density B at 90°
to the current, the conductor will experience a
force of magnitude I L B
This is the sum of the forces on all the electrons,
so the force F acting on each electron is given by
© David Hoult 2009
If there is a magnetic field of flux density B at 90°
to the current, the conductor will experience a
force of magnitude I L B
This is the sum of the forces on all the electrons,
so the force F acting on each electron is given by
F = ILB = IB
nA
nAL
© David Hoult 2009
Substituting for I gives
F =
© David Hoult 2009
Substituting for I gives
nALeB
F =
tnA
=
© David Hoult 2009
Substituting for I gives
nALeB
F =
tnA
=
LeB
t
© David Hoult 2009
Substituting for I gives
nALeB
F =
tnA
=
LeB
t
© David Hoult 2009
but L/t is
© David Hoult 2009
but L/t is the (drift) velocity of the electrons
© David Hoult 2009
but L/t is the (drift) velocity of the electrons
therefore
© David Hoult 2009
but L/t is the (drift) velocity of the electrons
therefore
F =evB
© David Hoult 2009
In general the magnitude of the force acting on a
charged particle moving with velocity v, at 90° to a
magnetic field of flux density B, is given by
F = qvB
where q is the charge on the particle
© David Hoult 2009
If the particle moves at angle q to the field
© David Hoult 2009
If the particle moves at angle q to the field
the magnitude of the component of its velocity at
90° to the field is
© David Hoult 2009
If the particle moves at angle q to the field
the magnitude of the component of its velocity at
90° to the field is v cos a
© David Hoult 2009
If the particle moves at angle q to the field
the magnitude of the component of its velocity at
90° to the field is v cos a = v sin q
Therefore, in general F =
© David Hoult 2009
If the particle moves at angle q to the field
the magnitude of the component of its velocity at
90° to the field is v cos a = v sin q
Therefore, in general F = q v B sin q
© David Hoult 2009
The Motion of Charged Particles in
Magnetic Fields
© David Hoult 2009
A charged particle moving parallel to the flux lines
© David Hoult 2009
A charged particle moving parallel to the flux lines
experiences no force
© David Hoult 2009
A charged particle moving parallel to the flux lines
experiences no force
There are three possible paths for a charged
particle moving through a uniform magnetic field
© David Hoult 2009
If the angle, q between the field and the direction
of motion is zero the path is
© David Hoult 2009
If the angle, q between the field and the direction
of motion is zero the path is a straight line
© David Hoult 2009
If the angle, q between the field and the direction
of motion is 90° the path is
© David Hoult 2009
If the angle, q between the field and the direction
of motion is 90° the path is circular
field into plane
of diagram
© David Hoult 2009
If the angle, q between the field and the direction
of motion is 90° the path is circular
field into plane
of diagram
© David Hoult 2009
If the angle, q between the field and the direction
of motion is 90° the path is circular
field into plane
of diagram
© David Hoult 2009
If the angle between the field and the direction of
motion is 0° < q < 90° the path is
© David Hoult 2009
If the angle between the field and the direction of
motion is 0° < q < 90° the path is
© David Hoult 2009
If the angle between the field and the direction of
motion is 0° < q < 90° the path is
© David Hoult 2009
If the angle between the field and the direction of
motion is 0° < q < 90° the path is a helix
© David Hoult 2009