measuring the strength of a magnetic field © david hoult 2009
TRANSCRIPT
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
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MotionThuMb
First finger
Second finger
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MotionThuMb
Second finger
FieldFirst finger
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MotionThuMb
Field
Current
First finger
SeCond finger
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© 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 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 current, I
F 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 current, I
F 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 current, I
F 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 current, I
F length of conductor, L
F = I L × a constant
magnetic field strength or magnetic flux density
© David Hoult 2009
F = I L B
© David Hoult 2009
F = I L B
units of B Newtons per Amp per meter, NA-1m-1
© David Hoult 2009
F = I L B
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 = I L B
units of B Newtons per Amp per meter NA-1m-1
The flux density of a magnetic field is
1 NA-1m-1 is called 1 Tesla (1 T)
© David Hoult 2009
F = I L B
units of B Newtons per Amp per meter NA-1m-1
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
1 NA-1m-1 is called 1 Tesla (1 T)
© David Hoult 2009
F = I L B
units of B Newtons per Amp per meter NA-1m-1
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
1 NA-1m-1 is called 1 Tesla (1 T)
© David Hoult 2009
Force acting on a charged particle moving through a magnetic field
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© 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
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In this piece of conductor there are
© David Hoult 2009
In this piece of conductor there are NAL free electrons
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If all these electrons pass through end x in time t then the current, I is given by
In this piece of conductor there are NAL free electrons
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n A L et
If all these electrons pass through end x in time t then the current, I is given by
In this piece of conductor there are NAL free electrons
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If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude
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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
I L B
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
n A LF = = I B
n A
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Substituting for I gives
F =
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Substituting for I gives
n A L e Bt n A
F = =
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Substituting for I gives
n A L e Bt n A
F =L e B
t =
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Substituting for I gives
n A L e Bt n A
F =L e B
t =
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but L/t is
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but L/t is the (drift) velocity of the electrons
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but L/t is the (drift) velocity of the electrons
therefore
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but L/t is the (drift) velocity of the electrons
therefore
F = e v B
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F = q v B
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
where q is the charge on the particle
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If the particle moves at angle to the field
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If the particle moves at angle to the field
the magnitude of the component of its velocity at 90° to the field is
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If the particle moves at angle to the field
the magnitude of the component of its velocity at 90° to the field is v cos
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If the particle moves at angle to the field
the magnitude of the component of its velocity at 90° to the field is v cos = v sin
Therefore, in general F = © David Hoult 2009
Therefore, in general F = q v B sin
If the particle moves at angle to the field
the magnitude of the component of its velocity at 90° to the field is v cos = v sin
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The Motion of Charged Particles in Magnetic Fields
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A charged particle moving parallel to the flux lines
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A charged particle moving parallel to the flux lines experiences no force
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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
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If the angle, between the field and the direction of motion is zero the path is
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If the angle, between the field and the direction of motion is zero the path is a straight line
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If the angle, between the field and the direction of motion is 90° the path is
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field into plane of diagram
If the angle, between the field and the direction of motion is 90° the path is circular
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field into plane of diagram
If the angle, between the field and the direction of motion is 90° the path is circular
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field into plane of diagram
If the angle, between the field and the direction of motion is 90° the path is circular
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If the angle between the field and the direction of motion is 0° < < 90° the path is
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If the angle between the field and the direction of motion is 0° < < 90° the path is
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If the angle between the field and the direction of motion is 0° < < 90° the path is
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If the angle between the field and the direction of motion is 0° < < 90° the path is a helix
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