### PHYSICS 2204 (Mr. J Fifield)

```PHYSICS 3204
(Mr. J Fifield)
UNIT 3: SECTION 3
Electromagnetic Induction
Electromagnetic
Induction
Magnetism
likely consisted of a nail wrapped with wire. When you
connected a battery to the wire, the nail attracted paper clips,
staples, and certain coins.
•
That the magnet worked only when the battery was
connected. This leads to a very interesting and profound
observation:
•
When electrons are still they have an electric field around
them (last section on electrostatics), but when electrons are
moving they have an additional field called a magnetic field.
Electromagnetic
Induction
• The electrons undergo two types of motion: spinning and
revolving.
•
This causes the atom to have a magnetic field around it. That
is, it is like a tiny, tiny magnet. The word for such a tiny magnet
is dipole, where di-pole means two poles, one is called a north
pole and one is called a south pole.
•
This magnetic effect is not the same for all materials. The effect
would be the same only if the electrons of all materials spinned
and revolved in the same way. As you can see from the picture
before, a couple of electrons in the same region can have a
canceling effect if they rotate in opposite ways. That is, if one
rotates clockwise while the other rotates counterclockwise, there
will be a canceling effect on the tiny magnetic field.
Electromagnetic
Induction
•
•
THE DOMAIN THEORY
In a substance such as iron which is strongly attracted by a
magnet, there must be something about the electron spin and
resulting dipoles that are additive in some way.
The little arrows represent the direction of the magnetic fields of
individual dipoles. Note that in small neighbourhoods the
dipoles have the same orientation. These small neighbourhoods
are called domains. Note from the picture that a domain is also a
dipole, that is, each domain has a north and south pole. This
piece of iron is unmagnetized because the magnetic fields of
different domains are in random
Electromagnetic
Induction
•
The magnetic fields of the domains of a magnet will be almost
perfectly lined up as shown in the next picture.
•
The picture also shows that a magnet is a very large dipole.
Electromagnetic
Induction
• The picture below shows what happens to the domains of the piece
of iron if it is stroked many times with a magnet. The strong
magnetic field of the magnet causes the domains of the piece of iron
to line up.
Not only do the domains line up, but some domains become larger.
•
The piece of iron has become a magnet. We say that it has induced
magnetism because the external field of the stroking magnet caused
the iron domains to line up.
•
Note: you should be able to see that any magnet, whether factory
made or home made, can have only a certain strength. Once all the
domains are lined up or nearly lined up, that's it! It can't become any
stronger.
Electromagnetic
Induction
•
If the piece of iron is snapped in two, you will have two magnets! Each
of the two pieces will have N and S poles.
•
Since the magnet was created by causing the domains to line up, the
piece of iron can be demagnetized by making sure that the domains take
up random directions once again. Two ways to do this are
1. By heating the iron
2. By submitting it to some other kind of shock which will cause molecular
disturbance.
Note: the piece of iron is always a magnetic substance. That is, It
always has magnetic characteristics, but it becomes a magnet only
when the domains are aligned.
Electromagnetic
Induction
Earth’s Magnetic Field
English physicist Sir William Gilbert suggested that Earth’s
magnetic field is created by the flowing motion of hot liquid
metals under Earth’s crust, as shown in Fig. 15.9B. This notion led
scientists to a better understanding of the cause of magnetic
character at the atomic level (see Section 15.4) The interaction
between a compass (a free-spinning permanent magnet) and
Earth’s magnetic field has been of great importance for navigators
around the world.
Electromagnetic
Induction
By examining how solid iron from lava flow is magnetized,
Geologists have determined that the direction of Earth’s magnetic
field has changed in the past. Layers of Earth’s crust from
different eras show that the domain directions are in opposite
directions. Earth’s North Pole is really a magnetic south because
the north end of a compass points to it. The magnetic field also
varies in strength over the earth's surface. It is strongest at the
poles and weakest at the equator.
Electromagnetic
Induction
Magnetic Properties
•
•
Substances that are attracted
Paramagnetic substances are attracted by a magnet. In such
substances the spin of one electron is not cancelled by
another. Paramagnetic substances that are strongly attracted,
are called ferromagnetic. Some ferromagnetic substances are
iron, cobalt and nickel. Other paramagnetic substances that
are attracted to a lesser degree are oxygen, aluminum and
platinum.
•
•
Subtances that are repelled
In some substances electrons are paired in such a way that the
spin of one cancels the spin of another. Such substances are
weakly repelled by a magnet and are called diamagnetic.
Examples are bismuth, zinc, silver and carbon.
Electromagnetic
Induction
Magnetic Fields
Using a compass it is possible to map a magnetic field as
shown. The direction of a magnetic field at a point within the
field is the direction that a compass points when place at that
location--in other words magnetic lines of force start at the
north pole and end at the south pole.
Electromagnetic
Induction
The Law of Magnetic Forces
Similar magnetic poles (north and north or south and
south) repel one another with a force, even at a
distance apart.
Electromagnetic
Induction
• Dissimilar poles (north and south or south and
north) attract one another with a force, even at a
distance apart.
Electromagnetic
Induction
Activity
• Read Text Pages: 627 - 632
• Extra Practice Questions: In your
textbook:
• on p. 638--do #1, #2 a, d, c, f
• on p. 663--do #6 - #8
Electromagnetic
Induction
MAPPING FIELD LINES
Recall that to map an electric or gravitational field, we
use a test charge or test mass, respectively. To map a
magnetic field, a compass is used It is used to detect the
presence of a magnetic field by applying the law of
magnetic forces. The north end of the compass is
repelled by the north pole of any magnet creating the
field.
Electromagnetic
Induction
The test compass maps the field lines around a simple bar
magnet by rotating its dipole to indicate the direction of force
that its North end experiences in the magnetic field at that
particular point in space. Magnetic field lines are drawn
tangent to the compass needle at any point. The number of
lines per unit area is proportional to the magnitude of the
magnetic field. The direction of the magnetic field is defined
as the direction in which the north pole of a test magnet
(compass) would point when placed at that location.
Electromagnetic
Induction
Using iron filings is equivalent to using many tiny
compasses with undefined poles. Notice how the magnet
is a dipole because each field line begins at one pole and
flows to the corresponding point on the opposite pole.
The law of magnetic forces dictates the convention that
field lines flow from the north pole to the south pole of
the field-creating magnet.
Electromagnetic
Induction
The Magnetic Field Around a
Straight Conductor
Demonstration
Question:
What does this indicate?
Electromagnetic
Induction
The Magnetic Field Around a
Straight Conductor
We have already said that when electrons move they
Have a field called a magnetic field.
Oersted, Hans (1777-1851), a Danish physicist, in 1819,
discovered the deflection of a compass needle while
near a current-carrying wire performing a
demonstration for his students. This discovery of a
connection between electricity and magnetism rocked
the scientific community.
Electromagnetic
Induction
The picture below shows the magnetic field around a
straight piece of wire with the current traveling from
left to right.
The magnetic field lines form concentric circles
around the wire. The direction of the magnetic field is
perpendicular to the wire and is in the direction the
fingers of your left hand would curl if you wrapped
them around the wire with your thumb in the direction
of the current. (Left-hand Rule)
Electromagnetic
Induction
• Imagine that the wire is bent so the back end is on the bottom
with the current going into the screen (the X represents the back
end of the current arrow), and the front end is on the top with the
current coming out of the screen (the dot represents the tip of the
current arrow).
•
Again use left-hand rule to confirm that the magnetic field is in
the proper direction. Note the region where the magnetic field
lines are in the same direction.
Electromagnetic
Induction
Cautionary Note
You are going to meet several left-hand rules. It is
extremely important to remember that left-hand rules
do not work for moving positive charges (only for
moving negative charges). Equally important, if you do
physics in college or university, you will likely be using
conventional current (flowing from + to - as pointed out
in Section 02, Lesson 01). Left hand rules do not work
for conventional current.
Electromagnetic
Induction
Now imagine that you have wrapped
it around a cardboard centre like the
one found in the centre of a roll of
toilet paper. The result will be
something like the picture (right).
again, and visualize what
you would "see" if the coil
were sawed down the
middle:
If you discard the half of the coil nearest you, will be left with
something like the picture below. On the top of the coil the current is
coming out of the screen , and on the bottom of the coil the current is
going into the screen. The magnetic field is shown for each turn of
wire.
Electromagnetic
Induction
Look more closely at the way the fields of each turn add together.
Inside the coil all the little fields add up to the left. On the outside
of the coil all the fields add up to the right. The end result can
pictured as follows.
If the coil is long and has many turns it is called a solenoid.
The magnetic field around a soleinoid is identical to that of a bar
magnet
Electromagnetic
Induction
Magnetic Fields around Current
Carrying Conductors (coils)
The direction of the field may be determined by the ‘Lefthand Rule for solenoids”.
Electromagnetic
Induction
Note
The location of the N-pole depends on more than the current
direction. It also depends on the way the turns are wound. Look at
the next coils carefully:
Electromagnetic
Induction
The strength of an electromagnet
• In elementary school, you very probably made an
electromagnet by wrapping wire around a nail or an
iron bolt.
•
The magnetic field around such an electromagnet
depends on the (i) direction of the current and (ii) the
direction in which coil is wound
Electromagnetic
Induction
Factors that affect the strength are:
• 1. the size of the current--the bigger the current, the stronger
the field
•
2. the number of turns in the coil--the more tightly wound the
coil is, the stronger will be the field
•
3. the size of the coil--the smaller the diameter, the stronger the
field
•
4. the type of core inside the coil--an electromagnet wrapped
around a ferromagnetic core will be much stronger than one
wrapped around a cardboard coil. The reason is that the
domains within the ferromagnetic core line up due to the
magnetic field passing through the centre of the coil.
Electromagnetic
Induction
• There is a term that accounts for the change in the
strength of an electromagnetic according to the type
of material that comprises the core. The term is
magnetic permeability, and it is represented by the
Greek letter mu (μ).
•
The relative magnetic permeability of a substance is
a ratio of the strength of the magnet when the core is
made of that substance to the strength when their is
no core at all.
•
Ferromagnetic substances have a high permeability.
You can find the magnetic permeability of some
familiar substances in Table 15.3 on p. 637 of your
textbook.
Electromagnetic
Induction
The Motor Principle
• Electric motors may look complicated when you look
at them, but the underlying principle is as simple as
this: if two magnetic fields are in the same vicinity,
they will act on each other. You already know this is
true for two permanent magnets depending on how
they are brought near, their magnetic fields either
attract each other, or repel each other. That is, one
magnet can make the other move. And that is the
basic operation of a motor: two magnetic fields make
the inside part of the motor move.
Electromagnetic
Induction
Only two magnetic fields are needed to make a motor.
The are two options:
1. the permanent field around a permanent magnet,
2. the field that we can start up and shut off around a
conductor.
Electromagnetic
Induction
Simple motor
In the first picture you can
see only one magnetic
field. There is no sign of a
circular field yet. This is
because the switch is
opened, there is no current
flowing, and no circular
magnetic field around the
straight conductor which
is hanging like a
motionless swing.
Electromagnetic
Induction
When the switch is closed, the current
flows and a circular pink magnetic field
is created around the conductor
according to left- hand rule #1. Look at
the black field and the pink field to the
left of the conductor. The black arrows
and the pink arrows are in the same
direction. This means the two fields
are repelling each other to the left of
the conductor. Look at the black field
and pink field to the right of the
conductor. The black arrows and the
pink arrows are in opposite directions.
Therefore in this region the fields are
attracting each other. The end result is
that the conductor is kicked to the
right. We have made motion out of
electricity and magnetism. We have
created a motor!!
Electromagnetic
Induction
The area where the
action takes place is
shown in a blow-up
below.
Study the picture until
you can see the fields in
the same direction to the
left of the conductor
(repelling); and the fields
in opposite directions to
the right of the
conductor (attraction).
The conductor will be
forced to the right.
Electromagnetic
Induction
left-hand rule #3. When a straight conductor is in a
magnetic field and is carrying a current, it will experience
a force. You can find the direction of that force like this:
point the fingers of your left hand in the direction of the
external (permanent) field. Point your thumb in the
direction of the current. Then your palm points in the
direction of the force on the conductor.
Electromagnetic
Induction
The picture below shows the action of a straight
current-carrying conductor placed between the
North and South poles of two bar magnets. Using
left- hand rule #3 you may predict the direction of
the force on the wire when (i) the current goes into
the screen, (ii) the current comes out of the screen
Electromagnetic
Induction
If you have ever taken a motor apart, you know that the inside
piece that rotates consists of many, many turns of wire. This is too
complicated to draw here, but we can show why the "rotor" rotates
by looking at just one of the turns of wire.
g" and "h" are brushes. "e" and "f" make up a split-ring
commutator with a half-ring attached to each end of the loop.
The brushes allow the current to pass into and out of the loop via
the split rings.
Electromagnetic
Induction
In the picture the loop is more
or less horizontal and a
current is flowing through the
loop. We have seen that the
loop will rotate because of the
interaction of the permanent
field and the induced circular
field.
question
What can you say about the current in the loop when the
loop has rotated ¼ of a complete rotation from its
present position? (Look at the picture carefully).
When the loop rotates 90o from its present position, the
gaps between the rings will be touching the brushes. No
current will flow for that split, split, split second.
Electromagnetic
Induction
Question
Will the loop stop after making ¼
turn?
No!! Inertia will keep it moving.
Question
Is the inertia required to make the
loop rotate very far?
Hardly anywhere.
Question
How come?
Because almost immediately split ring "e" comes in contact
brush "h", and split ring "f" comes in contact with brush
"g". When that happens, the current flows in the loop once
more.
Electromagnetic
Induction
Below shows the "end-on" view of the same loop.
You are looking directly into the screen.
Electromagnetic
Induction
The Motor Principle
Determining the size of the force on the
straight conductor
How may we increase the size of the
(green) force on the straight conductor?
That is, how can we make our motor more
powerful?
There are FOUR ways:
Electromagnetic
Induction
There are FOUR ways:
1. We can increase the size of the permanent magnets,
which will in turn increase the strength of the permanent
magnetic field (the vertical black lines). The symbol for
magnetic field strength is B. The larger B is, the larger the
force on the conductor will be, or F α B.
2. We can increase the size of the circular field that is
induced by the current in the conductor. This may be
done by increasing the current (I) in the conductor. The
larger I is, the larger the force on the conductor will be, or
Fα I.
Electromagnetic
Induction
3. If the length (L) of the conductor is increased, the fields that
interact are also effectively increased. The longer the conductor,
the more circular field there will be to interact with the permanent
field, therefore Fα L.
4. The force F is directly proportional to the sine of the angle that the
conductor makes with the permanent field: F α sin .
Electromagnetic
Induction
Finally, we put all of the proportions together to get
F α BIL sin .
The force (F) exerted on a straight current-carrying
conductor in a magnetic field of strength B is directly
proportional to the product of the strength of the field,
the current (I) in the conductor, the length (L) of the
conductor, and the sine of the angle that the conductor
makes with the field.
Choosing k as a proportionality constant permits the
following equation: F = k BIL sin , Now solve the
equation for B gives:
Electromagnetic
Induction
B has the unit Telsa in honour of engineer, Nicola Tesla
(1856-1943):
1 tesla (T) is the magnitude of the magnetic field
strength (B) that causes a conductor of length 1.0 m to
experience a force of 1.0 N when when the conductor is
carrying a current of 1.0 ampere and is perpendicular to
the magnetic field
Electromagnetic
Induction
Practice exercise 1
Calculate the magnitude of the force on a 2.1 m wire that is carrying
a current of 5.0 A perpendicular to a magnetic field of strength
1.4 x 10-4 T.
Solution
L = 2.1 m
B = 1.4 x 10-4 T
F=?
I = 5.0 A
= 90
F = BIL sin
= 1.4 x 10-4 T x 5.0 A x 2.1 m x sin 90
= 1.47 x 10-3 = 1.5 x 10-3 N
Working out the units:
Electromagnetic
Induction
Practice exercise 2
The wire (and current) in practice exercise 1 is running from
east to west. The magnetic field direction is from north to south.
In which direction will the force be exerted on the conductor?
Solution (method 1)
Left-hand rule #1 is used to draw the
circular field around the conductor. The
permanent (black) field and the pink
circular field are in the same direction
above the conductor, but in opposite
directions below the conductor.
Therefore, above the conductor the fields
repel each other, and below the conductor
the fields attract each other. The net force
on the conductor is therefore downward!
Method 2
Simply use The LHR #3
Electromagnetic
Induction
Practice exercise 3
Determine by what factor the force diminishes if a conductor
changes its orientation from being perpendicular to the
magnetic field to a new position that makes an angle of 45o with
the field.
Solution
Since the only thing that changed is
the angle, we write
L2 = L1
I2 = I2
1 = 90
2 = 45
B1 = B2
Determine F2/F1 :
When the conductor is at an
angle of 45o with the field, the
force on the conductor is less
than 75% of the force when the
conductor is perpendicular to
the field.
Electromagnetic
Induction
Practice exercise 4
A 3.0 m wire has a linear density of 0.020 kg/m. The wire is sitting in
a magnetic field of strength 3.5 x 10-3 T and the wire is perpendicular
to the lines of force. How large a current would be required in order
for the wire to be suspended against gravity in the magnetic field?
Solution
We know that gravity is pulling down with a force F =mg, and, if
the wire is to be suspended, the magnetic force (F= BIL sin) must
be pushing upward with an equal and opposite force. In other
words, BIL sin = mg.
L = 3.0 m
θ = 90o
B = 3.5 x 10-3 T
m = 3.0 m x 0.02 kg/m = 0.06 kg
g = 9.8 N/kg
I=?
Make the substitutions:
Electromagnetic
Induction
The Galvanometer--an Application of the Motor Principle
A galvanometer is an instrument used to measure very tiny currents.
It consists of a small coil of wire that can rotate in the magnetic field
of a permanent magnet.
In the picture. Use left-hand rule #2 to
confirm that for the given current, the N
and S poles of the coil are shown
properly. The poles of the coil are
attracted to the poles of the permanent
magnet and the coil turns so that the
pointer moves to the right of the zero
reading. When the current is turned off, a
restoring spring (not shown) pulls the
pointer back to zero. If the current source
is reconnected in reverse, then the N and
S poles of the coil switch ends, and the
pointer swings to the left of the zero
position
Electromagnetic
Induction
Activity
• Read Text Pages: 633 - 642
• Extra Practice Questions: In your
textbook:
• p. 650--do #1, #2.
• p. 663--do #10, #11.
• p. 664--do #25, #26
• p. 665--do #37
Electromagnetic
Induction
A little Review...
Remember, Hans Christian Oersted
discovered that the magnetic field
around a conductor appears as
shown.
The larger the current the stronger
the magnetic field, or B α I.
Also, The larger the distance the weaker the field. This is an inverse
relationship, written as
.
Combing the two we get
André Marie Ampere was interested in extending Oersted's
discovery to a more general situation where the conductor is not
necessarily a straight one, and the path around the conductor is not
a nice circle. The latter of these two conditions is shown in the next
picture.
Next slide....
Electromagnetic
Induction
In the second part of the picture
the path is broken into tiny
segments ΔL and each tiny path
segment has a small parallel
component of the magnetic field
strength B associated with it.
Ampere was able to show that the sum of the products of
was
directly proportional to the current I flowing through the closed path.
In other words, the larger the current, the bigger the sum of the little
products.
The proportionality can be written as an equation when a constant of
proportionality is inserted. Ampere was able to show that the constant
was a very special one: it was !! Recall that is the magnetic
permeability of the substance in which the field is located . The
mathematical form of Ampere's Law is therefore
Electromagnetic
Induction
The Magnetic Field (B) around a Straight Current Carrying Conductor
Now we will apply Ampere's general statement to Oersted's special
case where the pattern of the magnetic field is a perfect circle around
a straight conductor.
Since
everywhere on the uniform circular path,
and B can be factored out to give
Next…..
Electromagnetic
Induction
Note that the difference is in the presentation of the proportionality
constant.
As derived from Ampere's Law, k has a very special characteristic
that includes the magnetic permeability (μ) of the substance in
which the field is located. If the field is in free space, the μ is
written as μo where μo = 4 x 10 - 7 T·m/A. Air can be considered to
be free space.
The expression
is attributed to Jean-Baptiste Biot (17741862) and is called Biot's Law.
The law states that the magnetic field strength (B) is directly
proportional to the current in a straight conductor, and inversely
proportional to the perpendicular distance (r) away from the
conductor, with the constant of proportionality being μ /π2
Electromagnetic
Induction
Practice exercise 1
Find the magnetic field strength (B) in air 7.0 mm away
from a straight conductor in which there is a current of 2.0
A.
Solution
r = 7.0 mm = 7.0 x 10-3 m
I = 2.0 A
μ o = 4 x 10-7 T·m/A (air)
B =?
Electromagnetic
Induction
Practice exercise 2
When a potential difference of 12.0 V is applied to a
straight conductor, the magnetic field strength (B) 2.0 cm
from the conductor is 3.0 x 10-5 T. What is the resistance
of the conductor?
Solution
In Biot's Law there is no mention of voltage and
resistance. But there is mention of current. So, if we can
find the current, it will be easy to compute the resistance
(from Ohm's Law).
V = 12.0 V
o = 4π x 10-7 T·m/A (air)
R = ?
I before we can compute R)
B = 3.0 x 10-5 T
r = 2.0 cm = 2.0 x 10-2 m
I = ? (we must determine
Electromagnetic
Induction
Use Biot's Law to determine I. Use Ohm's Law to
determine the resistance of the conductor.
Solving Biot's Law for I gives
Then applying Ohm's Law:
R = V/I = 12.0 V / 3 A = 4.0 .
Electromagnetic
Induction
Practice exercise 3
Two parallel wires each carry 5.0
A of current in opposite
directions. What is the magnetic
field strength midway between
the wires if the wires are 10 cm
apart?
Solution
I1 = I2 = I = 5 A
r1 = r2 = r = 5.0 cm = 5.0 x 102 m
μo = 4π x 10-7 T·m/A (air)
B1 = ?
B2 = ?
Electromagnetic
Induction
Because of the identical givens, it is easy to see that B1 = B2.
Moreover, since B1 and B2 are in the same direction, the total
magnetic field strength midway between the wires will be B1 + B2.
The magnetic field strength midway between the wires is
B1 + B2 = 2 x 10-5 T
+
2 x 10-5 T = 4 x 10-5 T.
Electromagnetic
Induction
Activity
• Extra Practice Questions: In your
textbook:
• p. 663--do #17, #18
• p. 664--do #22. (To do part b, assume
that the wires are 2.0 cm apart)
•
Electromagnetic
Induction
Magnetic Force on Moving Charges
Review: you learned that 1 ampere of current represented a flow
of 1 coulomb of charge in one second; you also found out that 1
coulomb of charge was comprised of more than 6 billion electrons!
A new Definition: Using Magnetic Fields to define one Ampere
Two current carrying wires below each carries 1.0 A of current.
Also, the wires are 1.0 m long and are also 1.0 m apart. Remember
in air, the magnetic permeability is μo = 4π x 10-7 T·m/A.
Notice:
I1 = I2 = 1.0 A, therefore B1 = B2. Also the
magnitudes of F2 on 1 and F1 on 2 would be
equal even if the currents were different (due to
Newton's Third Law).
In the area between the wires, the fields are in
the same direction (out of the screen) and
therefore repel each other.
Electromagnetic
Induction
Notice:
.
I1 = I2 = 1.0 A, therefore B1 = B2. Also the magnitudes of F2 on 1 and F1
on 2 would be equal even if the currents were different (due to
Newton's Third Law).
In the area between the wires, the fields are in the same direction (out
of the screen) and therefore repel each other.
Electromagnetic
Induction
Now compute the magnitude of the green repelling force (F). Let B1 be
the permanent field.
Remember, according to the motor principle, wire #2 will experience a
force because it is carrying a current and lying in the magnetic field B1.
That force is F = F1 on 2 = B1 I2 L2 sin θ, where sinθ = 1 because the
downward current in wire #2 is perpendicular to the horizontal "circles"
of B1. This leaves us with F = B1 I2 L2.
Notice that the F is the force
that wire #1 is exerting on
wire #2. The right-hand side
of the expression tells us
this as well. There you will
see that the magnetic field of
wire #1 (that's B1) is acting
on the current and length of
wire #2 (that's I2 and L2 ).
Electromagnetic
Induction
The expression F = B1I2 L2 is not of much use because even though
we know I2 and L2 , we do not have the equipment to measure B1 .
This is where Biot comes in. Remember from earlier that the following
expression can be written for wire #1:
where r is the distance
from wire #1 to wire #2 and o is the magnetic permeability of free
space (in this case air).
Substituting Biot's Law into F = B1I2 L2 gives
At last we can calculate the magnetic
force that two 1.0 m wires exert on each
other when they each carry a current of
1.0 A and are 1.0 m apart.
Electromagnetic
Induction
And finally, a more satisfying definition of one
ampere of current:
One ampere (1 A) is the current flowing through
two parallel wires placed one meter apart in air
when the wires exert a force of 2 x 10-7 N/m on
each other for each metre of their length.
Electromagnetic
Induction
Exercise 1
Two wires are lying parallel to each other and 13 mm apart. One of
the wires is carrying a current of 3.5 A and the force between the
wires is 2.5 x 10-4 N/m. What is the current in the other wire?
Solution
r = 13 mm = 13 x 10-3 m
I1 = 3.5 A
F = 2.5 x 10-4 N/m
θ= 90o
μo = 4π x 10-7 T·m/A
L1 = L2 = 1.0 m (The lengths are not given. However, the force is
given as N/m, which dictates that the lengths must be one metre.)
I2 = ?
The force on one wire by the other is F = BIL sinθ where the B is
around one wire and the I and the L refer to the other. Also sin 90o =
1, so more specifically, F = B1 I2L2 .
Next……..
Electromagnetic
Induction
The other thing to remember is that B1 = (μo /2π) I1 and
substituting for B1 into F = B1I2 L2 gives
A similar exercise can be found on p. 647 of your textbook
where r is the unknown.
Electromagnetic
Induction
The other thing to remember is that B1 = (μo /2π) I1 and
substituting for B1 into F = B1I2 L2 gives
A similar exercise can be found on p. 647 of your textbook whe
Electromagnetic
Induction
The Magnetic Force on a Single
Moving Charge
We have seen that the force on a current-carrying conductor as it sits an
external magnetic field is F = BIL sinθ. The key is current-carrying. If
there were no current, there would be no force on the conductor.
So, the force is really exerted on the current. The conductor just
provides a path for the current. If a stream of electrons were shot through
a magnetic field the force on the stream would still be F = BIL sinθ, where,
in this case, L would be the length of the stream that falls within the
magnetic field.
Next we are going to determine the force on a single charged particle.
Instead of a current of electrons passing through a magnetic field,
imagine a single electron (charge q) being fired into the field. In fact the
single charge could be a proton, neutron or ion.
Continue Next slide...
Electromagnetic
Induction
Think: The charge q is traveling at a speed v and takes a time of t to
travel a distance L. Since distance = speed x time, we can write L = vt.
If there is a stream of electrons, and there are n charges of size q in the
stream, the total charge will be Q = nq.
Remember, that current is the rate of flow of charge. That is
So now
Use L = vt and I = nq/t to re-write F = BIL sinθ .
Electromagnetic
Induction
Summing up,
The magnetic force on an individual moving charge is given by the
equation F = Bqv sinθ where B is the magnetic field strength in tesla
(T), q is the magnitude of the charge in coulombs (C) that is moving
at a velocity v in m/s, and is the angle between
To determine the direction of the force apply left-hand rule #3: point
your fingers in the direction of the magnetic field, your thumb in the
direction that the charge is moving, then the palm of your hand
points in the direction of the force on the charge.
Electromagnetic
Induction
Practice exercise 2
A magnetic field of 44.0 T is directed into the screen. A particle with
a negative charge of 2.0 x 10-18 C is shot into the field from the right,
making an angle of 90o with the field lines. If the particle is moving
at 5.4 x 107 m/s, what magnetic force doe it experience?
Solution
B = 44.0 T
v = 5.4 x 107 m/s
F = ?
q = 2.0 x 10-18 C
= 90o
F = Bqv sin θ
= 44.0 T x 2.0 x 10-18 C x 5.4 x 107 m/s Sin 90o
= 4.8 x 10-9 N
The magnitude of the force is 4.8 x 10-9 N. Use left hand rule #3 to
determine the direction in which the particle is deflected. This
means the particle is deflected towards the top of the screen.
Electromagnetic
Induction
Moving Charges Circular motion
A particle moving at constant speed in a uniform magnetic field
where the field is perpendicular to the particles velocity will trace
a circular path. This means that the magnetic force will provide a
centripetal force to keep the particle in circular motion.
Where:
r: radius of curvature of particle, meters (m)
v: velocity of particle (m/s)
B: Magnetic Field Strength Tesla (T)
q: Charge on the particle (C
Electromagnetic
Induction
Practice Exercise 1
An electron travelling at 7.7 x 106 m/s enters into a uniform magnetic
field at a right angle. It is deflected in a circular path with a radius of
3.5 x 10-2 m. What is the magnitude of the magnetic field it
experiences? (PUBLIC EXAM, JUNE 2005)
Electromagnetic
Induction
Activity
Extra Practice Questions: In your textbook:
•
• p. 652--do #6--#8.
• When doing #8, substitute your right hand in
left-hand rule #3 because a proton has a
positive charge.
•
• p. 663--do #12, #14
• p. 665--do #31,
Electromagnetic
Induction
Assignment
Do research and prepare a written report on the applications of the
motor principle that are found in Section 15.6 of your text
(magnetohydrodynamics and the mass spectrometer)
it would be helpful to know the following:
Review:
- when a charge q is in an electric field E , the force that the electric
field exerts on the charge is F = qE . If the charge is an electron, then
the expression can be written as F = eE .
- when a charge q is moving perpendicular to a magnetic field B, the
force that the magnetic field exerts on the charge is F=qvB (because
sin =1.
- objects of mass m moving in a circular path are experiencing a
centripetal force which is expressed as F = mv2/r.
Electromagnetic
Induction
Michael Faraday discovered an exactly opposite phenomenon to
Oersted’s principle.
Faraday's Law: when a magnetic field moves near a conductor it
makes any free charge in the conductor move. --that is, a changing
magnetic field creates a current.
A magnetic field can change in two ways:
1. It can move physically. (i) if you move a bar magnet back and
forth, then its magnetic field also moves back and forth and (ii) the
magnetic field can remain stationary while the conductor itself is
moved back and forth.
2. It can also change by having its intensity or strength increased or
decreased. (ie. By changing the current through the coil).
Electromagnetic
Induction
The relative motion of the
conductor and the external
magnetic field has induced a
Important: either the
conductor must move, or the
magnetic field must move, or
the magnetic field must
change in intensity in order
that for the current to be
induced.
Electromagnetic
Induction
Here the path of the representative
electron (the red arrow) is now such that
the blue circular magnetic field is
perpendicular to the black permanent
field. Because the fields are
perpendicular, they cannot interact.
Therefore, the electron feels no force due
to the external field, and there will be no
induced current.
If the conductor is pulled through at
some angle, then there will be an induced
current greater than zero but less than
the maximum that results when the
conductor cuts the field lines at 90o
Electromagnetic
Induction
Alternating Current (AC)
A dry cell or battery is a source of electric current that travels only in one
direction. It is called direct current ( DC )
Alternating current does not travel in the same direction all the time. Neither
does the current have a constant magnitude.
A simple way to produce AC , can be seen
in Fig 16.2 on p. 670.
Also shown right.
As the magnet is pushed in and pulled
from the coil, the galvanometer needle will
show that the current reaches a maximum
in one direction, then goes to zero and
reaches a maximum in the other direction.
This illustrates that there is an alternating
current in the coil circuit.
Electromagnetic
Induction
Electromagnetic
Induction
The operation of the iron
ring is just an extension of
the picture before where the
magnet is moving in and out
of the coil.
The primary coil has a current (of if you like, voltage) source, and the
secondary coil does not. When the switch is closed a current begins
to flow and in a split second reaches a certain maximum amount. In
the short time that the current is "growing", a magnetic field will
"bloom" or expand around the primary coil. The primary coil
becomes, an electromagnet. As the primary field expands, its lines
of force will cut through the turns of the secondary coil. According
to Faraday's discovery, as the magnetic field cuts through the
secondary coil, a current will be induced in the secondary coil and
the galvanometer needle will move.
Electromagnetic
Induction
Remember a current is induced only as long as the magnetic field is
changing, that takes only a split, split, split second for the current in
the primary coil to reach some maximum reading. So, after the split
second, the galvanometer drops back to zero.
Now when the switch in the primary coil is opened, the current dies
away and therefore the magnetic field collapses. The force lines are
once again moving through the secondary coil, but in the opposite
direction. A current will be induced again, but this time in the
opposite direction. The galvanometer needle move opposite to the
original deflection when the switch was closed. This deflection
again lasts for the split second that it takes the current to drop to
zero. After that, there is no field around the primary.
If the switch is repeatedly opened and closed, the galvanometer
needle will indicate an alternating current, first one way, and then
the other.
Electromagnetic
Induction
Activity
• Read textbook page 670 -671
• Extra Practice Questions: In your
textbook: