A-LEVEL PHYSICS
Pupils should be able to:
•Understand a magnetic field as an example of a
field of force produced either by current-carrying
conductors or by permanent magnets.
•Represent a magnetic field by field lines.
The space surrounding a magnet where a magnetic
force is experienced is called a magnetic field.
A magnetic field in a permanent magnet can be
represented by magnetic field lines drawn so that:
(i) The line gives the
direction of the field
at that point.
(ii) The number of lines
per unit cross-section
area is an indication of
the “strength” of the
field.
S
Since the North Pole is repelled by the
north pole of a magnet and attracted by the
south, the arrows point away from the
North Pole and towards the South Pole.
N
The field round a bar magnet
varies in strength and direction
from point to point, i.e. is nonuniform.
S Magnetic field patterns in a N
bar magnet
The closer the
lines, the stronger
the field, and the
greater the force.
U-shaped
magnet
If two magnets are placed
near each other, their
magnetic fields combine to
produce a single magnetic
field.
(A)
Field pattern between two different poles
(B)
X
In diagram A, the poles of a
magnet would exert equal but
opposite force on a ‘free’ pole
placed at this point.
At point X, the field from
one magnet exactly cancels
out the field from the other.
X is known as NEUTRAL
POINT.
Field pattern between two similar poles
Field due to a current in a straight wire:A conductor carrying an electric current has
an associated magnetic field.
Field lines
For a straight wire the field lines are a
series of concentric circles centred on
the wire.
The right - hand screw rule is a useful aid
for predicting the direction of the field knowing the
direction of the current. It states:
If a right-handed screw moves forward
in the direction of the current
(convectional), then the direction of
rotation of the screw gives the direction
of the magnetic field lines. (Maxwell’s
screw rule)
Right – handed screw
Straight current-carrying wire
The direction of the field can also be found by using the
right-hand grip rule:
It states: grip the wire
using the right hand with
the thumb pointing in the
direction of the current –
the fingers then point in
the direction of the field.
Current direction
down into slide
Click here to
return to the
slide “field in a
long solenoid”
Magnetic field
in a flat
circular coil
Current direction
up out of slide
Continued -----------
Magnetic field in a flat / plane circular coil
N
S
Current
direction
You must note
that Maxwell’s
right hand screw
rule applies to
the field around
any short
section of the
coil.
Click here for grip rule
The field pattern produced by a current flowing in a circular coil is
similar to that produced by a short bar magnet, and the coil acts as if
it has a N pole on one face and a S pole on the other.
Click here to go back to slide “field
in a long solenoid”
N
S
When a current is passed through
a long coil or solenoid, each turn
acts as a single coil and produces
a magnetic field.
Click here to recap
field in a circular coil
Click here to recap
right hand grip rule
Together, the turns give a
combined magnetic field very
similar to the field around a long
bar magnet.
The coil behaves as if it has a N pole at one end and a S pole at the other.
The right-hand grip rule can be used to work out the polarity.
Click here to find out how ----
Click here to skip ---
The right-hand grip rule:
Imagine your righthand gripping the coil
in a way that your
fingers point the same
way as the
convectional current
arrows.
Your thumb then
points towards
the N pole.
Important: reversing the
direction of current
flow will reverse the
polarity of a solenoid.
Click here to go back to
“field in a long solenoid”
Thumb points to N pole
N
S
Fingers indicate convectional
current direction
To remember: Two rules for
determining the direction of a
magnetic field.
(i)
Right-hand grip rule for
current carrying solenoid
(ii)
Right-hand screw rule for
current carrying straight wire
To see “Animated effects” on this topic, visit
http://www.matter.org.uk/schools/start.html
Stronger magnetic field in a long solenoid:
For a solenoid of any given length, the strength of the
magnetic field can be increased by:
(i) Increasing the current
(ii) Increasing the number of turns on the coil
(iii) A soft ferromagnetic (e.g. iron) core. Solenoids of this
type are called ELECTROMAGNETS, and they have many
applications.
This train is running at a precise distance above
the track by computer-controlled electromagnets.
•
There is really no fundamental difference between these two ways of
creating magnetic fields.
•
All magnetic effects are due to electric currents.
•
In the case of permanent magnets, the field is generated by the
motion of electrons within the atoms. Each electron represents a
small current as it moves around within its atom, and this current
produces a magnetic field.
•
In the case of an electromagnet, the field is generated by the electrons
from a ferrous material such as iron combining with the current to
produce a stronger magnetic field.
Mr Vinay Thawait
M.Sc. M.Phil. P.G.C.E.
Pupils should be able to:
1.
Appreciate that a force may act on a current-carrying
conductor placed in a magnetic field.
2.
Define magnetic flux density (B) and the tesla (T).
3.
Recall and use force on a current F = BIL, with
directions as interpreted by Fleming’s left-hand rule.
4.
Use Fleming's left-hand rule to predict the direction
of forces acting on two long, straight, parallel current
-carrying conductors.
When a current is passed
through a conductor, a
magnetic field is produced.
Demonstration
A current carrying
wire in a magnetic
field.
When a current-carrying
conductor is placed in a magnetic
field, it interacts with any other
magnetic field and produces a
force.
N
S
N
S
Experiments shows that the force is always perpendicular to the plane
which contains both the current and the external field at the site of the
conductor.
The conductor in this case is a length of stiff copper wire, and it is at
right angles to the field provided by a U-shaped magnet.
When the switch is closed, a current flows through the wire.
The wire moves upwards, indicating that there is an upward force acting
on it.
If the direction of either the current or the field is reversed, the wire moves
downwards.
How can we find the direction of the force?
We can predict the direction of the
force using Fleming’s left-hand rule.
N
S
thumb
thrust (force)
Return to
learning
outcome
first finger
field
We use Fleming’s lefthand (or motor) rule to
predict the direction of
the force.
Second finger
current
(convectional)
If the thumb and first two fingers of the left hand are placed comfortably
at right angles to each other,
With the first finger pointing in the direction of the field and the second
finger pointing in the direction of the current flow (convectional),
then the thumb points in the direction of the thrust (force).
i.e. in the direction in which motion takes place if the conductor is free to move.
Points to remember, when applying the rule:
1.
2.
3.
The direction of the field is from the N pole to the S pole.
The direction of the current is from the positive (+) terminal of the
power pack to the negative (-) terminal, i.e. convectional current
direction.
The rule applies only where the current and field directions are at
right angles.
A force still acts if the current and field directions are at some
other angle, but its direction is more difficult to predict.
Demonstration
N
Field
Conductor
carrying current
out of screen
A current carrying
wire in a magnetic
field.
Force
N
Field
Force
Next learning outcome click
S
S
Conductor
carrying current
into screen
When a current carrying wire, that is free to move, is placed
in a magnetic field it will experience a force and the wire will
jump out of the field.
The
production of
this force is
known as the
motor effect,
because this
force is used
in electric
motors.
In a simple motor, a current flowing in a coil produces a magnetic field;
this field interacts with a second field produced by a permanent magnet.
Pupils should be able to:
1.
Define magnetic flux density and the tesla.
2.
Recall and use force on a current F = BIL, with directions as
interpreted by Fleming’s left-hand rule.
A useful way to think about a magnetic field is in terms of magnetic flux.
What do we mean by flux?
It is the measure of the number of magnetic
field lines passing through the region.
The word ‘flux’ means something that is flowing out of the north pole of a
magnet and travelling around to the south pole.
The lines of force can then be called flux lines.
So, what is the magnetic flux density (B)?
The density (strength) of a magnetic field depends on how concentrated
the flux is.
Where there is a lot of flux flowing, we say the field is strong.
Definition:
The magnetic flux density is defined as the force
acting per unit current in a wire of unit length at
right angles to the field.
or
We can say the magnetic flux density is the amount of flux flowing
through unit area at a point in the field.
The magnetic flux density is sometimes called flux density or magnetic
induction or B-field.
The symbol used for flux density is B and its unit is the Tesla ( T ).
The direction of the flux density at a point is that of the tangent to the field
line at the point.
The magnitude of the flux density is high where the number of field lines
per unit area is high.
Direction
of B at P
Field lines are parallel and therefore
B is constant, i.e. a uniform field.
Field lines close
together – B
large
B is small
Click here to go
back
In symbols, B is defined by the equation:
When a current I flows through a conductor of length l in a magnetic
field, it feels a force F. The stronger the field, the greater the force.
F
The strength of the field B is given in equation form by:
B = -------
SI unit of B is the Newton per ampere metre N A-1 m-1 .
Defining Tesla?
Il
1 T = 1 N A-1 m-1 .
A tesla is the magnetic flux density if a wire of length 1m carrying a
current of 1A has a force exerted on it of 1N in a direction at right
angles to both the flux and the current.
Force exerted 1N
“Diagram showing A tesla”
Uniform magnetic
flux density B
Wire of length 1m carrying a current of 1A
F
Rearranging the equation defining B we see that
B = ------the force F on a conductor of length l, carrying a
current I and lying at right angles to a magnetic
Il
field of flux density B, is given by:
F = BIl
If the conductor and field are not at right angles, but make an
angle  with one another the equation becomes:
F = B I l sin 
Where, F = the force on the conductor (N)
B = the magnitude of the magnetic flux density of the field (T)
I = the current in the conductor (A)
L = the length of the conductor (m)
The force on a current depends on the angle it makes with
the magnetic flux.

It is clear that the force on the conductor has its maximum value when the
conductor, the current and the external field are at right angles to each
other (  = /2 ).
and is zero when the conductor is parallel to the field ( = 0).
Back to previous slide
Q1.
In an electric motor a rectangular coil of wire has 150 turns and is
0.20 m long and 0.12 m wide. The coil has a current of 0.26 A
through it and is parallel to a field of magnetic flux density 0.36 T.
Find the force exerted on the coil.
Ans: 0.0187 N
click here
Q2.
A straight wire is placed in a uniform magnetic field of magnetic
flux density 0.023 T at an angle of 30° with the magnetic field. The
wire carries a current of 8.6 A. Calculate the force on a 3.4 cm
length of the wire. Show the direction of the force in a diagram.
Ans: 0.0034 N
click here
Click here for next page
Ans 1.
Force F on 0.20 m of wire with 0.26 A through it is given by:
F = BIl
= 0.36 X 0.26 X 0.20
= 0.0187 N
Ans 2.
F = B I l sin 
= 0.023 X 8.6 X 0.034 X sin 30°
= 0.0067 X sin 30°
= 0.0034 N
Force exerted
If currents flows
in the same
direction through
two parallel wires
as in the diagram,
there is a weak
attraction
between them.
A
Maxwell’s screw
rule gives direction
of field
B
Fleming’s left-hand
rule gives direction
of force
Each wire
experiences a
force because
each carries a
current and
each is in the
magnetic field
produced by
the current in
the other wire.
Wire A produces a magnetic field whose
direction is given by Maxwell’s screw rules.
Knowing this direction, and the direction of current through B, the
direction of the force on B can be found using Fleming’s left-hand rule.
The force is to left.
A similar argument shows that the force on wire A is to
the right.
If the currents flow in opposite directions, they repel each other.
X
L
Y
Fleming’s left-hand rule
gives direction of force
F
B
Maxwell’s screw rule
gives direction of field
The ampere is the
constant current which,
when flowing through two
infinitely long, straight,
parallel conductors which
have negligible areas of
cross-section and are 1
metre apart in a vacuum,
causes each conductor to
exert a force of 2 X 10 –7 N
on each metre of the
other.
Like currents attract and unlike currents repel.
Forces between current-carrying conductors provide the
basis of the definition of the ampere.
1.
Magnetic fields are produced by permanent magnets and by electric
currents. This can be represented by lines of force.
2.
When a current flows across a magnetic field, there is an interaction
between the two fields.
3.
The direction of the resulting force is given by Fleming’s left-hand rule.
4.
The strength of a magnetic field is known as the magnetic flux density.
5.
The force on a current-carrying conductor in a magnetic field is given by:
F = BIl
6.
and
F = B I l sin 
There is a force between two parallel currents, and this is used as the
basis of the definition of the ampere.
Mr Vinay Thawait
M.Sc. M.Phil. P.G.C.E.