Magnetism
- a magnet has polarity. It has 2 ends. A north
seeking end (north pole) and a south seeking end
(south pole).
- a compass is a small magnet on a pivot so that it is
free to rotate.
Like poles repel and unlike poles attract.
A magnet will attract other metal objects (paper clips,
nails). Either end will attract these objects.
The object becomes polarized. The direction of
polarization depends on the polarization of the magnet.
This is similar to the polarization induced in a
conductor by a charged particle.
Microscopic examination reveals that a magnet is
actually made up of tiny regions known as domains.
Each domain behaves like a tiny magnet with a north
and a south pole.
You cannot "break" magnets into separate "monopoles".
Poles always come in pairs.
Permanent magnets are made of ALNICO. Aluminum,
nickel, and cobalt. There are also rare earth elements,
neodymium, that produce extremely strong permanent
magnets for their size.
Permanent magnets are fragile. Dropping them will
cause the domains to disorient.
Heating them weakens the magnet. Once cooled, it will
regain its strength unless heated past the “Currie
point”. The magnet will be totally destroyed. (p. 755
Currie point table)
The forces between magnets occur when magnets
touch but also when they are at a distance. The same
way electric and gravitational forces are explained by
fields.
Magnetic forces can be explained by the existence of a
magnetic field, B. Magnetic field lines are imaginary
like electric field lines.
The number of magnetic field lines passing through a
surface is called magnetic flux.
Flux per Area is proportional to the strength of the
magnetic field lines.
- flux lines are concentrated where the magnetic field
is the greatest – poles.
Lines come out of the north pole and in at the south
pole. Lines always form closed loops because there are
no isolated poles on which field lines start or stop.
Electromagnetism
In 1820, Hans Christian Oersted found that the forces
on the poles were perpendicular to the direction of
current in a wire. He also found that when the charges
were stationary (no current was moving through the
wire), no magnetic forces existed.
The magnetic field of a current carrying wire can be
shown:
Circular lines indicate that magnetic field lines form
closed loops.
You can find the direction of the field using
FIRST right hand rule (p. 756):
- keep thumb pointed in direction of current flow.
Your fingers point in the direction of the magnetic
field, B.
Take a coil of wire. When an electric current flows
through the coil, it has a field like a permanent magnet.
The coil (solenoid) has a north and a south pole. This is
called an electromagnet.
Ex. A magnetic compass is held directly above a
straight conductor that is lying across this page.
If electrons flow from left to right in the conductor,
towards which edge of the page does the north-seeking
pole of the compass point:
a) to the top
b) to the left
c) to the right
d) to the bottom
The direction of the field of an electromagnet is found
using
SECOND right hand rule (p. 764):
- grasp the coil with your right hand with fingers
pointing in direction of current. Your thumb points
towards the N pole of the magnet.
To increase the strength of an electromagnet, place an
iron core inside the coil.
- the coil magnetizes the iron core by induction.
- the magnetic strength of the core adds to that
of the coil.
strength of field α current & # of loops
Basic Law of Magnetism:
two magnetic fields will interact to produce forces
of attraction (opposite poles) and repulsion (similar
poles).
Forces caused by magnetic fields:
Ampere suggested that there should be a force on a
current-carrying wire placed in a magnetic field.
Faraday discovered the force on the wire is at right
angles to the direction of the magnetic field and to the
direction of the current.
The direction of the force on a current carrying wire is
found by
THIRD right hand rule (p. 770)
- point the fingers of your right hand in the
direction of the magnetic field. Point your thumb
in the direction of the conventional current flow in
the wire. The palm of your hand faces the
direction of the force acting on the wire.
Force on a Wire due to a Magnetic Field
The magnitude of the force on the wire is proportional
to three factors:
i) the strength of the magnetic field, B
ii) the current in the wire, I
iii) the length of the wire that lies in the
magnetic field, L. L= nl where n is the number
of turns in the coil and l is the length of the
individual turn.
F = BIL sin θ
Units - Tesla, T
The strength of the magnetic field, B, is called
magnetic induction.
Force on a moving charge:
F = Bqv sin θ
Ex. 1 A particle carrying a charge of +2.50 µC enters a
magnetic field traveling at 3.40 x 105 m/s to the right
of the page. If a uniform magnetic field is pointing
directly into the page and has a strength of 0.500 T,
what is the magnitude and direction of the force acting
on the charge as it just enters the magnetic field?
Ex. 2 A wire segment of length 40.0 cm, carrying a
current of 12.0 A, crosses a magnetic field of 0.75 T
(up) at an angle of 40.o right. What magnetic force is
exerted on the wire?
Oersted discovered that an electric current produces
a magnetic field.
In 1822, Michael Faraday was able to show that a
changing magnetic field could produce electric current.
When the switch was closed (ie. steady current), there
was no deflection on the galvanometer. Faraday
noticed a deflection only when he closed OR opened the
switch.
A CHANGING magnetic field can produce an electric
current. This is the induced current.
The relative motion between the wire and the magnetic
field produces current. The process of generating
current through a circuit is electromagnetic induction.
Basic principle of electromagnetic induction:
whenever the magnetic field in the region of a
conductor is moving or changing in magnitude,
electrons are induced to flow through the
conductor.
When the magnetic field through the coil changes, a
current flows as if there were a source of EMF
(electromotive force) in the circuit.
A battery or any device that transforms one type of
energy (mechanical, chemical) into electrical energy is a
source of EMF.
Inside the battery or device, there is internal
resistance. No matter how efficient the device, there
will be energy losses inside the device.
The potential difference, V, inside the battery (caused
by chemical reactions) is the EMF.
IF THERE IS NO CURRENT FLOWING, the terminal
voltage is equal to the EMF.
When Faraday moved a magnet through the coil, he
generated electrical energy (induced a current).
This electrical energy came from the moving magnet
(kinetic energy).
This transfer of energy is WORK. Work required a
force.
To remove KE (gain EE) requires a force that acts in
the opposite direction to the motion of the magnet.
Lenz's Law (1834) is the law of electromagneticmechanical opposition.
For motion, Lenz’s law states that if a loop of wire
moves while inside an external magnetic field then a
current is produced in the moving wire that will
produce its own magnetic field.
This magnetic field will interfere with the external
magnetic field in such a way that the two fields will try
to oppose the motion (change in position of the moving
loop of wire).
- the N pole of a magnet is moved toward the right end
of a coil. To oppose the approach of the N pole,
the right end of the coil must also become a N
pole.
Ex.
One way to produce an electric current through a
conductor is to move a conducting rod through a
magnetic field.
x x x
x x x
x x x
x x
x x
x x
A voltage is induced in the
rod (e- move to one end of
the rod).
v
When there is a voltage in the rod, it becomes part of
an electric circuit.
x x x
x x x
x x x
x x
x x
x x
l
The rod acts like a battery.
v
The magnetic force on the conducting rod must be in
the opposite direction to its motion (opposite v).
V = Blv
Flux: the number of magnetic field lines (Φ).
Faraday said that the induced voltage is proportional to
the rate of change in the magnetic flux.
Φ = B⊥ A cosθ
units are Tm2 Wb (Weber)
∆Φ
V=
∆t
. . . . . . . . .
. . . . . . . . .
. . .∆
∆A. . . . v.
l
∆x
conductor
∆Φ = B ⊥ l ∆ x
∆x
∆t
V = B ⊥ lv
v=
If you have loops of wire,
V = −N
∆Φ
∆t
This corresponds to Lenz's law.
If Lenz’s law were not true, the change in flux would
produce a larger current which would produce a
greater change in flux…
The current would continue to produce power even
after the original stimulus ended. This violates the law
of conservation of energy.
Direct Current - an electric current in which the net
flow of charge is in one direction only.
Ex. Battery
Alternating Current - an electric current that
reverses its direction with a constant frequency.
A graph of current vs time has the form of a sine
wave.
A number of practical devices make use of the force
that exists between a current and a magnetic field.
Ex. Outlets
Galvanometer - device to measure very small currents.
Consists of a small coil of wire placed in the strong
magnetic field of a permanent magnet. Each turn
of the wire is a loop. The current passing through
the loop goes in one side of the loop and out the
other side. One side of the loop is forced down
while the other side is forced up (third RH rule).
The loop has torque and rotates.
Motor – changes electrical energy into mechanical
energy
Generator – changes mechanical energy into electrical
energy
DC Electric Motor
• Has a coil with an iron core ⇒ ARMATURE
• It is surrounded by magnets (electromagnets)
Two difficulties:
1.
2.
The magnetic forces are aligned directly
opposite each other and will no longer experience
a torque.
If you could change the direction of the current,
the coil would again experience a torque.
If the coil keeps turning, the leads will twist and
eventually break.
Solution:
• Use a split ring commutator (brass or copper)
• The armature is attached to the commutator so
they rotate together. One end of the coil is
connected to each half of the commutator.
• Brushes slide on the commutator to pass current
from the battery to the coil.
• DC current comes from the battery.
• The split ring goes from one brush to the other
causing the armature to rotate.
AC Electric Motor
• Uses slip rings as commutator.
• Since the current is alternating, the motor will
run smoothly only at the frequency of the sine
wave.
• The magnetic field is sinusoidally varying, just as
the current in the coil varies.
⇒ they do not require a split ring because the
current reverses itself.
Electric motors are mostly AC because our electric
energy for industry and home is transmitted as AC.
DC motor – starter motor on a car.
AC Generators
Generators are essentially the same design as
motors.
• The mechanical energy input to a generator
turns the coil in the magnetic field.
o This produces an emf (voltage).
o A sinusoidal voltage output.
The mechanical energy may come from:
i. Steam
ii. Wind
iii. Waterfall
iv. Electric motor
DC Generator
• The commutator must change the AC flowing
into its armature into DC.
o Commutators keep the current flowing in
one direction instead of back and forth.
Faraday’s study of the iron ring:
Open/close the switch to induce the current in a
second coil.
⇒practically, we don’t need to open/close the
switch constantly produce current in second coil.
⇒vary the magnetic field. To do this, we need
an alternating current.
The current produced by an AC generator provides
a means for the current to be turned on and off
without manually operating a switch.
Faraday’s iron ring is a TRANSFORMER.
• The voltage, V, induced in the second circuit
can be changed by changing the number of
windings around the ring in either circuit.
POWER PRODUCTION
Generators were built by Tesla to generate electricity
reliably and in large quantities.
Most of today’s energy sold is in the form of AC
because it can easily be transformed from one voltage
to another.
Power is transmitted at high voltages and low current
without much energy loss (heating of wire) because it
can be stepped down from the plant to many cities, to a
city, to the household.
Household typical outlet is 120 V AC.
Transformers are used to transfer energy from one
circuit to another by means of mutual inductance
between two coils.
Transformers consist of a primary coil (input) and a
secondary coil (output).
Step-up Transformer – secondary has more turns
- greater V induced, lower I
Step-down Transformer – primary has more turns
- less V induced, greater I
V
# turns
V
p
Vs
=
p
=
p
Vs
# turns
turns
p
turns
s
=
s
Is
Ip
• Transferring energy from one coil to the other OR
the rate of transferring energy is the power.
• The power used in the secondary is supplied by the
primary LAW OF CONSERVATION OF ENERGY
Therefore,
P into primary = P out of secondary
(VI )p = (VI )s