Download Magnetic Fields

AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
Magnetic Fields
Lessons
Topics
1
Magnetic flux density
Force on a current-carrying wire in a magnetic field.
F = B I l, when field is perpendicular to current.
Fleming’s left hand rule.
Magnetic flux density B and definition of the tesla
2 to 3
Moving charges in a magnetic field
Force on charged particles moving in a magnetic field.
F = B Q v when the field is perpendicular to velocity.
Circular path of particles; application in devices such as the cyclotron.
4 to 5
Magnetic flux and flux linkage
Magnetic flux defined by Φ = B A with B normal to A.
Flux linkage as NΦ where N is the number of turns cutting the flux.
Flux and flux linkage passing through a rectangular coil rotated in a magnetic
field: flux linkage NΦ = BAN cosθ where θ is the angle between the normal to the
plane of the coil and the magnetic field.
Current Carrying Conductors in a Magnetic Field
Magnetic field revision
The way that we refer to poles and the Earth’s
magnetism leaves a lot of room for confusion as I’m
sure you remember from year 8.
-1-
AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
A magnetic field is _________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
______________________________________________(see page 106)
We always draw the field lines running from north to south, and we say that these lines of forces
(magnetic field lines) are lines along which a free north pole would move.
What causes the Earth’s magnetic field? ______________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
Force on a current in a magnetic field
When a current carrying wire (moving charges) is in a field it experiences a force, as long as it isn’t
in line with the field lines. It will be at a maximum when at 900 to the field line.
We use Fleming’s left hand rule to remember how the forces direction is related to the current and
field.
-2-
AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
This is called the motor effect and is a result of the interaction of the two fields.
The strength of a magnetic field is usually measured in terms of a quantity called the magnetic flux
density of the field, B. A definition of B requires a consideration of the forces produced by
electromagnetic fields.
As we have already mentioned when a wire carrying a current is placed in a magnetic field the wire
experiences a force due to the interaction between the field and the moving charges in the wire.
A very good demonstration is the so-called catapult field experiment in which a wire carrying a d.c.
current can be made to move in the field of two flat magnets.
Before considering the mathematical nature of the forces on currents in magnetic fields it is worth
just looking at the simple magnetic field diagrams that give rise to these effects. These are shown in
Figure 1. (a) is the field between two magnets, (b) the field due to a current in a straight wire and (c)
the resulting field if they are put together. This last field is known as the “catapult” field because it
tends to catapult the wire out of the field in the direction shown by the arrow.
Fig 1
The force F on the wire in Figure 1 (c) can be shown to be proportional to
(a) the current on the wire I,
(b) the length of the conductor in the field L,
(c) the sine of the angle that the conductor makes with the field q, and
(d) the strength of the field - this is measured by a quantity known as the magnetic flux density B of
the field. The force is given by the equation:
Force on current in magnetic field: F = BIL sin θ
If we keep things simple and consider the current at 900 to the field then the formula is:
F = BIL
-3-
AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
The units for B are tesla (T) which is equal to _________________________________
The flux density of a field of one tesla is therefore defined as the force per unit length on a
wire carrying a current of one ampere at right angles to the field.
-4-
AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
Coils and Couples
If a coil carrying a current is placed in a magnetic field it will experience a force on two of its sides in
such a way as to make the coil rotate. This effect is the basis of all electric motors and moving coil
meters. Think of all the places where electric motors are used from stereos, disc drives, CD players,
starter motors in cars, washing machines etc. etc. and you will realise how important this effect is!
The forces are shown below.
If we coil wire together we can increase this force and with current running in opposite directions we
can create a “couple” – this is a very basic motor.
The d.c motor consists of:
(a) a number of coils of fine wire wound on
(b) a laminated soft iron armature
(c) a set of brushes to allow current to enter and leave the
windings;
(d) a commutator to reverse the current in the coils;
(e) a set of external field coils.
If we start with the coil in the position shown in diagram
Figure 2(a) then there will be an upward force on side (1) of
the coil and a downward force on side (2) of the coil. The coil
will therefore start to twist in an anticlockwise direction.
The inertia of the coil and core keeps it turning until the input
wires make contact with the ends of the coil again. This time
the positive wire touches side (2) and the negative wire
touches side (1). (Figure 2(b)).
Side (2) now moves up and side (1) moves down — the coil
continues to turn in an anticlockwise direction. This process
then continues and so the coil spins.
Complete summary question on page 109
-5-
AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
Moving Charges in a Magnetic Field
Electric current in a wire is caused by the
flow of negatively charged electrons. These
charged particles are affected by magnetic
fields – so a current- carrying wire moves in a
magnetic field.
1. The equation for the force exerted on a current-carrying wire in a magnetic field
perpendicular to the current is:
Equation 1:
2. To see how this relates to the charged particles moving through a wire, you need to know
that electric current, I, is the flow of charge, Q, per unit time, t.
3. A charged particle which moves a distance l in a time t has a velocity, v:
4. So, putting the two equations together gives the current in terms of the charge flowing
through the wire:
Equation 2:
-6-
AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
If the direction of motion of a charged particle in a magnetic field is at angle θ to the lines of the
field, then the component of B perpendicular to the direction of motion of the charged particle,
Bsin θ, is used to give F= BQvsin θ

If the velocity of the charged particle is perpendicular to the direction of the magnetic field, θ
= 90o so the equation becomes

If the velocity of the charged particle is parallel to the direction of the magnetic field, θ = 0o
so F =
Example
What is the force acting on an electron travelling at 2 x 104ms-1 through a uniform magnetic field of
strength 2T? (The magnitude of the charge on an electron is 1.6 x 10-19C)
Explain what a Hall Probe is.
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
Complete questions 1 +2 page 112
-7-
AQA A2 Physics A Unit 4
Magnetic Fields
D Ewart
The Movement of Charged Particles in Magnetic Fields
Sketch a diagram of an electron moving in a uniform magnetic field of flux density B. The electron
of charge e, enters the field with a velocity v.
The electron experiences a force at right angles to both the field and to its instantaneous velocity.
Use Fleming’s Left Hand Rule to judge the direction of the force
The electron experiences no acceleration in the direction of its existing velocity as the force is at
right angles to this direction.
The electron does experience an acceleration at right angles to its existing velocity.
When the electron has changed direction, the direction of the force that it experiences will also
change: the force will always be at right angles to its current velocity.
The magnitude of the new force is the same as the old force since the electron has not changed
its speed.
In other words, the electron will travel in a circular path. The centripetal force that causes the
circular motion is F
The radius, r, of the circular path can be found by equating the expressions for centripetal force and
for the force on a moving charge in a magnetic field:
Where m is the electron’s mass. Rearranging this equation gives:
-8-
AQA A2 Physics A Unit 4
Magnetic Fields
The cyclotron (pg113 &114)
Using a diagram explain how a Cyclotron Works
Using a diagram explain how a Mass Spectrometer Works
Complete questions 1 – 4 page 115
-9-
D Ewart