Download Magnetic FieldsThe Motor Effect and Induction File

Magnetism
• The region round a magnet where a magnetic
force is experienced is called a magnetic field.
• The field around a magnet can be plotted with a
small compass.
• The resulting lines are known as lines of force,
• The lines of force have a direction. It is the
direction that a north pole would move if placed
in the field.
S
N
Flux density
• The concentration of lines of force is a
measure of the strength of a magnetic field
and is known as the flux density (B)
• The unit of flux density is the tesla (T).
• The tesla is an extremely large unit.
The strength of the Earths magnetic field at the surface is around 10-5T
Region of lower
flux density
S
N
Region of
high flux
density
Direction of field lines
• Field lines always exist between the north
and south poles of a magnet or magnets.
• The convention is that field lines are drawn
from north to south.
• Field lines can never cross.
S
N
S
N
Neutral point
N
S
X
S
N
Neutral points occur where the sum of
the fields is zero
When a bar magnet points north in the Earth’s field there are points where the
Earth’s field and the field of the magnet sum to zero and form neutral points.
S
N
NORTH
THE MAGNETIC FIELD OF THE EARTH
On a large scale the Earth’s field is non uniform
Earth’s local magnetic field appears
uniform locally. This is how a
compass behaves as it is moved
across a lab bench
This is only the horizontal component of the field
There is also a dip angle θ is around 680 in the north of
England. So a compass on its side points down at this
angle.
θ
The Earth’s magnetic field is deviated by “ferromagnetic”
materials like iron, nickel or cobalt
Soft iron in the Earth field
magnetic fields of electrical origin.
• An electric current always has an
associated magnetic field.
• The field around a single straight wire is
made up of concentric lines of force
The field
around a
straight wire
current
current
The direction of the field is
remembered
by the corkscrew rule
The convention for current into the paper (left) and out of the paper (right)
X
COILS
The strength of the magnetic field is a vector quantity. In a
coil the “sense” (direction) of the field lines are the same and
add and the result is a field in which the lines are almost
parallel in the centre.
Around a helical coil (solenoid) the field is startlingly similar to
the field around a bar magnet.
The field inside a solenoid
An easy way to remember the
poles of a solenoid given the
direction of the current looking
at each end of the coil.
The motor effect
S
N
S
N
t
F
Field
I
S
thrust
N
S
Current
N
Vectors here add
positively
The current is into the page
N
S
Vectors At this
side cancel
field
N
S
thrust
This combination of field’s is sometimes referred to as a “catapult field”
The force on a current carrying
conductor
N
S
Calculating the force on a
conductor in a perpendicular
magnetic field
L
Force
Flux
density B
I
L is the length of the
conductor within the
field.
F = BIL
I is the current through
the conductor.
Exam Question
At a certain point on the Earth’s surface the
horizontal component of the magnetic field is
1.8 x 10-5 T. A straight piece of wire 2m long
with a mass of 1.5 g lies on a horizontal woodn
bench in an East-West direction. When a very
large current flows in the wire momentarily it is
just sufficient to cause the wire to lift off the
surface of the bench.
1. State the direction of the current in the wire.
2. Calculate the current in the wire.
3. What other noticeable effect will this current
produce?
Exam Question
At a certain point on the Earth’s surface the horizontal component of the magnetic
field is 1.8 x 10-5 T. A straight piece of wire 2m long with a mass of 1.5 g lies on a
horizontal woodn bench in an East-West direction. When a very large current flows
in the wire momentarily it is just sufficient to cause the wire to lift off the surface of
the bench.
1.
State the direction of the current in the wire. To the East
2.
Calculate the current in the wire. F=BIL, so I=F/BL
F= (1.5 x 10-3 x 9.81)N
I= (1.5 x 10-3 x 9.81)/(1.8x10-5 x 2)
I=410A
3. What other noticeable effect will this current produce?
The wire melts.
Current into the board
Field
Thrust on
wire
N
S
+ 134.95
There is a downward force on the conducting
rod. It is fixed and cannot move.
By Newton’s first law there is an equal and
opposite force on the magnetic “yoke” and the
yoke is pulled up.
This reduces the force on the balance and the
reading goes down
N
S
+ 119.48
134.95
Exam Question
The magnitude of force in a current carrying
conductor in a magnetic field is directly
proportional to the magnitude of the
current in the conductor. With the aid of a
diagram, describe how you could
demonstrate this in a school laboratory.
1. Diagram of a conductor perpendicular to a magnetic field (1)
2. Method of providing, varying and measuring d.c. current. (1)
3. Method of measuring variable force (eg top pan balance) (1)
4. For various values of current measure the force produced (1)
5. Plot F against I and straight line through origin (1)
F=BIL
FI
F/N
Gradient = BL
I/A
Defining the Tesla
The tesla is defined in terms of the moter effect of
a conductor in a magnetic field.
Current 1 A
Field 1T
1N
One tesla is the magnetic flux density of a field in which a force of
1 newton acts on a 1 metre length of a conductor which is
carrying a current of 1 ampere and is perpendicular to the field.
Two current carrying wires with current in the same direction have magnetic fields in the same sense.
When they are brought close together they experience an attractive force
This is because the field vectors cancel in the area between them and the
resultant force on each wire is towards the other.
We may think of a “catapult” field at both sides.
This is because the field vectors cancel in the area between them and the
resultant force on each wire is towards the other.
deflecting charged particles
Electric currents are no more than flows of charged particles in
conductors, so it is no surprise that magnetic fields can deflect the
paths of moving charged particles.
Thrust
S
Field
+
N
Current
deflecting charged particles
When negatively charged particles flow, the conventional current is in
the opposite direction.
S
Field
N
Current
Thrust
deflecting charged particles
The effect on a particle with a steady velocity is to push it in a circular
path at right angles to the field. The path returns to a straight line when it
emerges from the field
S
-
N
v
F
This has the implication that
Energy is not transferred by the field to the particle as the force on the
particle is always at right angles to the direction of its travel. This always the
case in circular motion
The charge on the particle is q and
its mass is m
v
r
The force towards the
centre is also given by
Because the particle is undergoing
circular motion, the force towards the
centre is:
mv
F
r
2
F  Bqv
B = magnetic flux density (T)
q is the charge (C) on the particle. (If
the particle is an electron this symbol
is written as e)
v is the velocity of the particle (ms-1)
Electromagnetic Induction
Magnetic Flux
• The magnetic flux is important in understanding electromagnetic
induction.
• The magnetic flux (Φ) is a measure of the number of field lines
passing through a region.
• The unit of magnetic flux is the weber (W)
• It is a vector quantity
A
A uniform
magnetic
field has a
constant
density of
field lines
throughout
B
In a uniform field the
number of field lines
passing through the
larger region B is
greater than through
the smaller region A.
Therefore we can say
that there is a greater
flux through B than A
Magnetic Flux
Here the magnetic flux is the
same in region A and B.
Sometimes a measure of
magnetic flux can be
misleading.
Magnetic Flux
• Below the magnetic flux through region A
is greater than through B because the
density of the field lines is greater.
A
B
The relationship between B and Φ
B
A
If the magnetic field is perpendicular to a region with area A, and the flux
density is B, Then the flux Φ in that region is given by:
Φ = AB
Moving a conducting wire in a
magnetic field
• If a wire is moved in a magnetic field such that field lines
are cut an emf is induced between the ends of the wire
An emf is induced between the ends of
the wire
An emf is NOT induced between the
ends of the wire
N
N
S
S
The direction of the induced emf
S
N
Direction of induced
emf
field
emf
motion
Induced e.m.f and moving
electrons
Motion of the bar
A
Magnetic field
Force tends to move
electrons in this direction
C
As we saw with free electrons moving in a field, they experience a force
as show in the diagram
+++
A
++
-----C
Here we see that conventional current will be driven from C to A if the
circuit is complete. i.e. the direction of the emf is from C to A.
The direction of the induced emf
S
N
With a closed
conducting loop, the emf
induced drives a current
through the loop
Here a current is induced in the single turn coil
in the same way.
N
If a current flows it always produces a field which opposes the motion of
the coil. In this case a north pole is induced on the face of the coil being
pulled towards the magnet.
This is a consequence of the law of conservation of energy. It always
applies. It is known as Lenz’s law.
Again as a consequence of Lenz’s law
When the coil is withdrawn a south pole is produced to oppose the motion
of the coil.
N
Note that if a North pole had been produced instead, the coil would
be repelled and the current due to induction increased. This would
cause further repulsion. We would have built a perpetual motion
machine! We would get energy for nothing in contravention of the
law of conservation of energy.
Coils With More Turns
Where the coil has more than one turn, the
magnetic flux through the turns of the coil is
called the flux linkage.
N
When a magnet moves through the coil, each
turn of the coil cuts the magnetic field by the
same amount.
So the flux linkage is just the
sum of flux through each turn.
If the magnet is moved with the same speed.
2 turns, → 2 x emf
3 turns → 3 x emf etc.
A
S
N
North pole induced at the
top of the coil on approach
A
G
North pole induced at the
bottom of the coil on leaving
S
Induced
emf/V
N
A
V
Time/s
The direction of the emf is reversed as the induced poles of the coil are
reversed. The bar magnet is accelerating so the rate of flux cutting is higher as
the magnet leaves the coil, hence the larger amplitude of emf for a shorter
time.
Faraday’s Law of Electromagnetic
Induction
1. The e.m.f. induced
in a coil depends on
the rate of change
of flux through the
coil.
N
The faster the flux changes the
greater the e.m.f. induced
Ε
Φ
t
Faraday’s law of electromagnetic
induction
• The e.m.f. induced is
proportional to the
number of turns in the
coil
N
N
ΕN
Faraday’s law of electromagnetic
induction
ΔΦ
ΕN
Ε
Δt
So combining these relationships
ΔΦ
ΕN
Δt
The units of the SI system combine in such a way that
the constant of proportionality is 1

ΕN

t
The expression to the right of the = sign is just the
rate of change of flux linkage
Faraday’s Law
ΔΦ
Ε  N
Δt
E is the e.m.f. Induced (V)
N is the number of turns on the coil
∆Φ is the change in flux though each turn of the coil. (Wb)
∆t is the time taken for the flux change.(s)
Note that in this equation the total change in flux linkage in the coil is N∆Φ.
Sometimes you may see this written as ∆NΦ.
It follows that 1 weber is the flux linkage in a coil if an emf of 1V falls
evenly to zero in 1 second
Using Faraday’s Law
A coil of 200 turns and 3cm in diameter lies perpendicular to a uniform
magnetic field with a flux density of 2 x10-2 T. The field falls evenly to 0T in
1s. Calculate the emf generated:.
1. Calculate the flux
through 1 turn of the coil
  BA
  .02T  .003m2  6 104Wb
2 Now apply Faraday’s law
V

ΕN
t
(610 4 )
Ε  200
 0.12V
1
Some effects of induction
The effect of a changing field on an
aluminium ring
d.c. supply to coil
When the d.c. supply is
switched on, there is a
change in flux through the
aluminium ring. An emf is
induced in the ring with a
field opposed to the coil.
The ring is repelled and
rises. As soon as the
current is steady though
the coil there is no further
change in flux and the ring
falls back.
When the circuit is broken, the flux changes again through the ring and
the ring is repelled again in accordance with Lenz’s law.
The effect of a changing field on an
aluminium ring
ac. supply to coil
When the a.c. supply is
switched on, there is a
continuous change in flux
through the aluminium ring.
An emf is induced in the
ring with a field opposed to
the coil. This field reverses
every time the field in the
coil reverses.The ring
continues to be repelled.
Electromagnetic damping
Electromagnetic damping
Electromagnetic damping
Electromagnetic damping
BACK EMF
When the coil L is connected in series with the cell V it produces an increasing
magnetic field as the current through the coil rises. This induces a “back emf” in
the reverse direction to the emf produced by the cell.
The magnetic field stores energy transferred from V
When S is moved so that L is in series with R only, the back emf
drives a current through R dissipating the energy stored.