Download P30 Forces and Fields Student_notes

Unit 2 – Electric and Magnetic Forces and fields
Unit 2A–Electric Forces and Fields
Electrical forces between static charges (stationary charges) have been
known since 700BC. –Amber
At the time of the renaissance, electricity was studied more completely.
Electrified substances fell into 2 categories (positive and negative)
while neutral substances formed a third category. These two categories
are used to state the Law of Electric Charges1. opposite electric charges attract each other
2. similar electric charges repel each other
3. A charge object can attract some neutral objects!!!??? Why?
To understand electrical charge, it is necessary to understand
something about the structure of matter.
1. all matter is composed of atoms
2. Atoms are composed of smaller particles called electrons,
protons and neutrons.
a. Electrons are negative
b. Protons are positive – same magnitude as electron
c. Neutrons are neutral
3. Protons and neutrons are found in a tight cluster at the centre
of the atom called the nucleus. Electrons are unclustered and
occupy the remainder of the atom with great freedom of
movement.
4. Protons and neutrons have about the same mass while an
electron has about 1/2000 the mass of either.
5. Atoms are electrically neutral because the number of protons
is equal to the number of electrons.
6. An atom can gain or lose electrons. Protons and neutrons are
neitherlost nor gained without a nuclear reaction occurring!
They are tightly bound in the nucleus.
a. Substance that gains electrons is called a negative
substance
b. Substance that loses electrons is called a positive
substance (net charge)
 explain qualitatively, the distribution of charge on the surfaces of
conductors and insulators
Conductors- materials in which electrons can move easily from atom to
atom –mostly solids (why?), some liquids and gases (ionic-aq or
capable of being ionized)
-charge spreads out quickly in conductors to the best
configuration for the repelling charges.
-best conductors are metals.
Insulators – materials in which electrons cannot move easily from atom
to atom – some solids, many liquids, but most gases – why?
-charge remains localized for insulators. (stays where you put
it)eg. Balloon
-they don’t transfer or release a charge very quickly.
http://www.youtube.com/watch?v=LfJywoeIIUI
conductor)
(charges on a hollow
Methods of Charging
****Electric charges on solids are due to an excess or shortage of
electrons.
 Explain electrical interactions in terms of the law of conservation
of charge
 Explain electrical interactions in terms of the repulsion and
attraction of charges
 Compare the methods of transferring charge
How to transfer a charge to an object:
1. Charging by friction
Electrons are held in an atom by attraction to the nucleus.
Depending on the types of atoms in a substance, it may have
a stronger/weaker attraction to its electrons. When two
materials of different strengths are rubbed together, the
‘stronger’ substance will take electrons from the weaker
one leaving them both with net charges.
- if it gained the electrons
+ if it lost them
The two substance have equal, opposite charges!! – Law of
conservation of charge. The two are attracted
2. Charging by conduction (contact)
When one object already has a charge, it can be used to
charge another object. This is done by bringing it into physical
contact (touching) it to the other objects. Some of the electrons
move and therefore some of the charge is transferred. The two
objects collectively have the same charge as the original object
(shared the charge).
For our purposes, the two objects will be of the same
material and so the charge is shared equally. Equal, same
charges on the objects. (objects repel)
However, what happens if the two objects are different
materials?
3. Charging by Induction
On a solid conductor, some of the negative charges are fairly
free to move. If a charged object is brought near to the conductor,
the electrons in the conductor will move giving the neutral
conductor opposite induced charges on each of its sides.
The neutral conductor can be given a permanent charge by
grounding it while the charge object is nearby.
Reverse scenario:
When charged by induction, the once neutral conductor has
a charge opposite to the charged object. (the two are attracted)
What happens to the charge on the charged object??? Anything?
How do the results of each method compare – similarities/differences?
Problems pg 82-84
COULOMB’S LAW
 Explain qualitatively the principles pertinent to Coulomb’s torsion
balance experiment
 Apply Coulomb’s law, quantitatively, to analyze the interaction of
two point charges
 Determine, quantitatively, the magnitude and direction of the
electric force on a point charge due to two or more other point
charges in a plane
 Compare qualitatively and quantitatively, the inverse square
relationship as it is expressed by Coulomb’s law and by Newton’s
universal law of gravitation.
 Analyze data and apply mathematical and conceptual models to
infer the relationship among charge, force and distance between
point charges. Use free body diagrams. Use graphical techniques
(such as straightening) to analyze data.
Coulomb (1736-1806) used a torsion balance to study electrical forces.
A thin metal wire is used to balance an insulating rod at its centre. On
either end of the rod are two identical spheres which can be charged.
Coulomb changed the distance between a charged rod and the torsion
apparatus and measured the angle of twist in the apparatus. The
amount of twist was considered proportional to the electrical force
between objects. He found that Fα 1/d2.
He also investigated the relationship between force (twist) and the
magnitude of the charge on the rod. He found that Fα q1 q2.
Combining these two results gives Coulomb’s Law for electrical forces;
F = kq1q2/r2
k is Coulomb’s constant of 8.99 x 109 Nm2/C2.
 Use free-body diagrams to describe the forces acting on a charge
in an electric field
*Coulomb’s Law only applies to point charges.
*Force is vector but it is often easier to use absolute values for charge
and apply a direction to force after solving for the magnitude (absolute
values).
Eg.
Two electrostatically charged
1
objects attract:
35o
Three objects of different charges
Interact.
m=20g
What if one objects distance or charge is changed? What happens to the
force?
Problems pg 86-94
Similarities/Differences to Fg – Newtons’ Law of Gravity
-both vary inversely with the distance squared.
-both involve a constant but the gravitational one is MUCH smaller 
-gravity is associated with mass, electrostatic is associated with charges.
-gravity is always attraction, electrostatic can be attraction or
repulsion.
Graphs (straightening, slope to find k or q)
Field Theory
 Define vector fields
 Compare forces and fields
 Explain, quantitatively, electric fields in terms of intensity
(strength ) and direction, relative to the source of the field and to
the effect on an electric charge
 Plot electric fields using field lines for point charges, combinations
of point charges and parallel plates
The concept of a field is used to explain how one object can influence or
affect another object even when the objects are not in contact. The field
theory is just a theory.
A field is defined as a sphere of influence and may be scalar
(magnitude only) or vector (magnitude and direction). Scalar fields
include sound and heat while vector fields include gravity, electricity
and magnetism.
Electric Fields
An electric charge exerts a force on anything around it. This region of
influence is called a field – it is a vector field with both magnitude and
direction.
Because electric forces may be forces of attraction or repulsion, the
direction of an electric field must be defined. (Unlike gravity)
Since a field can be drawn/defined without having any object within the
field, then the direction of an electric field is defined as the direction
taken by a positive test charge placed within the field. Consequently
the direction of an electric field is always away from the positive and
towards the negative –regardless of what objects are in the field!
Note: The strength of a field is represented by the density of the arrows
and the direction of the field is represented by the direction of the
arrows.
What would determine how strong a field really is?
-the amount of charge in the object
-the distance from the object
therefore: E=kq1/r2
where q is the charge on the object producing the field in
question.
DO NOT confuse E with energy!! It is electric field strength and
distinguished by the arrow on top of it.
This leads to a new formula:
By replacing the same variable in the Fe equation, you get
F=Eq
problems pg 97-105
Potential Difference - Parallel Plates:
 Compare qualitatively, gravitational potential energy and electric
potential energy
 Define electric potential difference as a change in electric
potential energy per unit of charge
 Calculate the electric potential difference between two points in a
uniform electric field
 Describe quantitatively the motion of an electric charge in a
uniform electric field
 Explain, quantitatively, electrical interactions using the law of
conservation of energy
 Analyze quantitatively the motion of an electric charge following a
straight or curved path in a uniform electri field using Newton’s
second law, vector addition and conservation of energy
The equation for electric field; E=kq1/r2 and force; F = kq1q2/r2 are for
static/point charges only. They cannot be used to describe the electric
field between two charged plates.
To describe the field between these plates we need the concept of
potential difference. When charged objects are allowed to move in an
electric field they always accelerate from a place of higher potential
energy to a place of lower potential energy because of the electric force
acting on it (like an object falling due to gravity). To move an object
opposite to this requires work so we will incorporate the work formula:
Work = force x distance
W= Fe x d but Fe = q E
so W=q E d Like with gravity, work done
to move an object against the force is stored in the object as potential
energy. So the increase in the potential energy is equal to the work!
∆Ep=q E ∆d
When a charged object is placed in a uniform field, it will move from a
place of high potential to a place of lower potential. It will lose potential
and gain kinetic. Potential difference is defined as the change in
potential energy per charge but can be calculated using either the
change in potential or kinetic for a conservative system since what is
gained in kinetic is lost in potential and vice versa (law of conservation
of energy).
∆V = ∆E/q
units for potential difference are J/C or V
Potential difference is much more useful in electricity than
kinetic/potential energy since it focuses on each charge instead of a
total. Like energy, it is scalar.
A battery is a source of PD. It is designed to move charges/ions from a
place of high potential to a place of low potential, therefore creating
movement of charges – electricity in a circuit. It converts chemical
potential energy to electrical (kinetic) energy.
Combining the two formulas learned today, we can come up with:
E = ∆V/∆d
another formula for calculating the electric field strength - this time,
between parallel plates. Remember, the field strength is uniform
(constant for a system)!
battery symbol
- +
Eg.
Problems pg 108-117
More Electric Plate Questions:
Calculate the speed of the 3.50x10-12C sphere of mass +4.00x10-15kg just as it
reaches the negative plate.
2.25x103V
+
-
+
An electron beam is projected between two parallel charged plates as shown below.
There is a 2.80x103 N/C electric field between the plates. Calculate the horizontal
distance the beam will travel before hitting the positive plate.
Negative plate
Electron beam
2.00 cm
e-
6.00x106m/s
5.00 cm
3.00 cm
Positive
plate
Physics Principles used to solve this question?
MILLIKAN’S OIL DROP EXPERIMENT:
 Explain Millikan’s oil-drop experiment and its significance relative
to charge quantization
The electron was discovered by J.J. Thompson early in the 1900’s (Unit
4). Soon afterward Arthur Millikan found the charge on an electron
called an elementary charge. It was discovered that an electron and a
proton had charges of exactly the same magnitude.
These discoveries were made by the use of parallel plates, electric force,
and fields.
How? Millikan sprayed oil droplets between two horizontal plates
which were connected to a variable (adjustable) voltage source. The oil
droplets were electrostatically charged from the spraying process so
that when they were between the plates they were affected by opposing
forces – gravity and electricity.
Note: When dealing with parallel plates we don’t generally concern
ourselves with gravity’s effect on the object because the electrical one is
so much greater. However, Millikan used a low voltage source and oil
drops (which have a much higher mass than a subatomic particle) so
that the electrical force was very weak and gravity’s effects played an
important role.
By adjusting the low voltage source, Millikan was able to suspend some
of the oil drops. For these suspended drops,
Fe = F g
Eq=mg
q = mg/E
How did Millikan find the mass on the oil drop? By using a ‘ruler’
behind the setup he could estimate the droplets diameter – allowing
him to calculate the volume. Then using his oil’s density (mass/volume)
he found the mass of the droplet.
E was found using the voltage of the power supply and the distance
between plates.
g is constant
From this formula, Millikan calculated a charge on the oil drop. This
however could be any multiple of the elementary charge. So Millikan
did the experiment many times and was able to determine that all the
calculated charges were multiples of 1.60 x 10-19C. He therefore
assumed that this was the smallest possible charge – elementary charge
- the charge of an electron and proton.
Problems pg 119-127
Review 131-133
CIRCUITS – Current/Voltage/Power
 Define electric current as the amount of charge passing a
reference point per unit of time
Current electricity involves new concepts because the charges are
moving. Modern current electricity describes the flow of electrons
(negative charge) based on our understanding of the atom and the
ability for electrons to be released.
Old theory described the flow of positive charge as being opposite to
modern theory. This is called ‘conventional current’. (used in the
textbook).
Electrical Current: the rate at which electrons move through a
conductor. The symbol for current is I and the unit is amperes (A).
I = q/t
One ampere = one coulomb/sec
Electrons do not move through a conductor unless there is a potential
difference. This potential difference that exists between the power
supply entry/exit must be consumed within the circuit (by resistor(s)).
For an electric current to operate there must be a voltage power source
and a complete pathway for the charges.
The amount of current in a circuit/conductor depends on the potential
difference and the resistance of the conductor.
More voltage more current (direct)
Less resistance  more current (inverse)
I = V/R
Resistance in a conductor (indicated by heat produced) depends on
several factors:
1. Type of conductor –some hold onto their electrons more –
more resistance
2. Cross-sectional area – smaller diameter of wire allows for less
flow of electrons – more resistance
3. Length of conductor – longer conductor – resistance increases
4. Temperature - most conductors have an optimal temperature.
Too high means random motion of electrons and vibration of
atoms so that it is difficult for electrons to flow –higher
resistance.
Electrical Power:
Power is the rate at which work is done or energy is used. Power is
measured in watts (W) where one watt = one J/s
P = W/t or ∆E/t
In electricity ∆E =q∆V
So:
Unit 2B -Magnetic forces and fields:
 Describe magnetic interactions in terms of forces and fields
 Compare gravitational, electric and magnetic fields in terms of
sources and directions
Lodestone is a naturally occurring magnetic rock. A piece of lodestone
will always line up in a north-south direction if it is free to move.
Lodestone was studied extensively and it was concluded that Earth
itself acted like a large lodestone and that was why a small piece of
lodestone always lined up in a north-south direction.
The ends of a magnet are called the N-pole (seeks earth’s geographic
north) and a S-pole (seeks earth’s geographic south). There are two
magnetic poles just as there are two kinds of electric charge. However,
unlike electricity it is not possible to isolate one magnetic pole.
Law of Magnetic Poles:
1. There are two kinds of poles, north and south
2. Like poles repel
3. Unlike poles attract
Similar to electric charges, magnets have a region of influence called a
magnetic field. Magnetic fields are vector fields (it has both magnitude
and direction). The direction of a magnetic field is defined as the
direction taken by a free north pole (*there is no such thing!). It is also
the direction that the north end of a compass would point!
S
N
S
N
S
N
N
S
S
N
N
S
S
N
Electric charges will affect small bits of almost anything in their electric
field. Magnets, however, only affect a few materials (mainly metals) in
their magnetic field.
http://www.youtube.com/watch?v=NJUTUFAWfEY
magnetic storm video
Magnetism and Electricity:
 Describe how the discoveries of Oersted and Faraday form the
foundation of the theory relating electricity to magnetism
 Describe, qualitatively, a moving charge as the source of a
magnetic field and predict the orientation of the magnetic field
from the direction of motion
Oersted discovered a relationship between electricity and magnetism
when he noticed that an electric current will deflect a compass needle.
The only way this can happen is if an electric current produces a
magnetic field. The field is circular around the wire. If the direction of
the current is reversed, the direction of the field is reversed.
1st left hand rule: determines the direction of the magnetic field around
a straight conductor.
 Hand is in relaxed position (curled)
 Thumb of left hand points in the direction of electron flow.
 Fingers circle the conductor in the direction of the magnetic
field.
X
Out of page
into page
If the straight conductor is bent into a loop, the magnetic field inside the
loop (coil) is made stronger.
Increasing the number of coils also increases the strength of the field.
This can create an electromagnet!
Electromagnets:
Electromagnets (solenoids) are made up of many loops of wire.
Electromagnets act like permanent magnets except they can be turned
on and off, and their strength can be easily adjusted. How?
The field surrounding an electromagnet is stronger inside the coil and
weaker outside the coil. The field also runs in opposite directions inside
vs outside the coil.
*electromagnet needs an insulator between the coils and a conducting
core to prevent current from flowing the shortest path through the core
conductor.
2nd left hand rule: determines the direction of the field for an
electromagnet.
 Hand is in relaxed position (curled)
 Fingers of left hand curl around the coil in the direction of
electron flow.
 Thumb points to the direction of the electromagnet’s north pole.
(this is the direction of the field inside the coil and opposite to the
field outside the coil)
Magnetic Fields/forces around Conductors (moving charges):
 Describe and explain, qualitatively, the interaction between a
magnetic field and a moving charge and between a magnetic field
and a current-carrying conductor
 Explain, quantitatively, the effect of an external magnetic field on
a current-carrying conductor
 Design an experiment
If two straight conductors are running parallel and are carrying current
in the same direction, they will attract one another:
If they have current in the opposite directions they will repel one
another:
The unit of current was actually defined in terms of this effect: One
ampere is the amount of current in each of two conductors that are one
meter apart and cause a force of 2 x 10-7 N to act on each meter of wire.
When two magnetic fields are overlapping, they will interact and create
a force. Another example of this is:
Below the conductor, the two fields have the same direction so they will
repel. Above the conductor the fields are opposite and will attract. The
net result is that the conductor is forced upwards (deflected).
Oersted discovered this relationship between current and magnetic
fields.
A short cut for determining the direction of deflection is the 3rd left
hand rule:
 Flat hand is used
 Fingers are pointed in the direction of the
permanent magnetic field.
 Thumb points in the direction of the current
flow (or particle velocity)
 Palm faces the direction of deflection.
Note: all three are perpendicular to each other.
Electric Motors make use of this interaction in order to convert
electrical energy (current) into mechanical energy (movement). In the
motor, a loop of wire (armature) becomes an electromagnet when the
current is turned on. This armature is placed in a permanent magnetic
field and so the two fields interact and cause a force that results in the
movement of the armature. Motor Effect
Because of the split-ring commutator and brushes, the polarity of the
armature reverses every 180o. This allows the armature to constantly
be repelled and continue to turn. (However, if an AC power supply is
used, then the motor does not need the split ring commutator since the
current is constantly reversing direction.)
To calculate the force of deflection on a conductor in a magnetic field:
Fm = B I l
Moving Charges in Magnetic Fields:
 Explain, qualitatively and quantitatively, how a uniform magnetic
field affects a moving electric charge, using the relationships
amoung charge, motion, field direction and strength, when motion
and field directions are mutually perpendicular
 Explain, quantitatively, how uniform magnetic and electric fields
affect a moving electric charge, using the relationships amoung
charge, motion, field direction and strength, when motion and
field directions are mutually perpendicular
 Analyze, quantitatively, the motion of an electric charge following
a straight or curved path in a uniform magnetic field, using
newton’s second law and vector addition
 Analyze, quantitatively, the motion of an electric charge flowing a
straight path in uniform and mutually perpendicular electric and
magnetic fields, using Newton’s second law and vector addition.
 Use free-body diagrams to describe forces acting on an electric
charge in electric and magnetic fields.
Charges passing through magnetic fields may also be deflected by the
magnetic field in the same way as charges in a conductor. To determine
the direction of deflection use the 3rd rule and apply it to your left hand
for negative particles and your right hand for positive particles. The
magnetic force is:
Fm = B q v
In a strong magnetic field they may be deflected so much that they end
up travelling in a circle:
In this case Fm = Fc
Charged particles in space are often deflected by Earth’s magnetic field.
Some of the particles are trapped in a spiral. When they reach the
atmosphere they collide with the gas molecules causing them to glow.
This creates the Aurora (northern/southern lights) near the poles of
Earth.
Why would this not occur at other latitudes?
Electromagnetic induction: (Generator effect)
 Describe, qualitatively, the effects of moving a conductor in an
external magnetic field, in terms of moving charges in a magnetic
field.
 Design an experiment
After Oersted’s discovery that an electric current produced a magnetic
field, it was discovered that a magnetic field could produce an electric
current .
An electric current can be produced in a conductor by moving the
conductor through a magnetic field. A voltage is induced across the
conductor. If the conductor is part of a circuit it will act like a battery.
Producing an induced voltage in a conductor using a magnetic field is
known as Electromagnetic Induction.
A current can be produced in an air core solenoid when a magnet is
moved in or out of the core. (demo)
When the magnet changes direction so does the current.
The direction of the induced current can be found using Lenz’ Law; the
magnetic force on a conducting rod is in the opposite direction to its
motion (the applied force).
Eg. When a magnet is pushed into a coil a current will move in a
direction such that the magnetic field inside the coil opposes the
magnetic field of the magnet. This must occur in order to satisfy the
conservation of energy principles. The two fields must oppose one
another or else you would be creating more energy!
Rod moved through a magnetic field will produce an electric current:
Loop of rod (generator)
4th left hand rule: used to find the direction of the induced current.




Use a flat hand
The palm is pointed opposite to the velocity of the rod.
Fingers point in the direction of the magnetic field
Thumb will point in the direction of the induced current in
the rod.
The strength of the current depends on the speed of the rod/magnet,
the amount of conducting rod/wire in the permanent field, and the
strength of the permanent field.
Another way to produce an electric current is by using an induction coil.
Michael Faraday used this to generate a brief current when the switch
was being closed or opened.
The current needs to be changing to cause the magnetic field to
fluctuate in the soft iron core AC current . This changing magnetic field
is similar to moving a magnet and therefore causes an induced AC
current on the secondary side.
A transformer (induction coil) is often used to convert a potential
difference to a higher or lower value.
Primary coil – connected to the power supply.
Secondary coil – no power supply – current is generated by induction.
If the number of coils on the secondary side is more than the primary,
the potential difference is increased on the secondary side. This is
called a step-up transformer. Eg. TV
If the number of coils on the secondary side is less than the primary, it
is called a step-down transformer. Eg. Transformer boxes outside your
home.
However, like lenz’ law, you can’t create more energy! So if we can
increase the potential difference by increasing the # of coils, something
has to decrease – current! This means the power/energy remains
constant.
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