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Physics I - a Review
Distance (fundamental): 3 dimensions; requires
VECTORS
Time (fundamental)
Mass (fundamental)
Motion (combines distance and time)
Forces cause changes in motion (Newton’s Laws of
Motion); types of force
Work and Energy (Conservation of Energy)
Power (rate at which energy is used or transported)
Momentum (used in collisions & explosions)
Physics I - a Review
Rotations (force  torque, mass  moment of
inertia, distance  angle; KE, angular
momentum)
Fluids (force  pressure, fluid flow and energy,
friction and viscosity)
Heat (flow of energy – power; relate to motion of
molecules, temperature)
Waves (flow of energy - waves on a string, sound
waves; power and intensity)
Physics II – an overview
Electricity (basic force of nature; voltage;
circuits)
Magnetism and electromagnetism (motors and
generators)
Light – moving energy (reflection, refraction,
lenses, diffraction, polarization)
Light – how we make it: leads to atomic theory
Nuclear force - inside the atom: (two basic forces
of nature) radioactivity and nuclear energy
Electricity - An Overview
In this first part of the course we will consider
electricity using the same concepts we
developed in PHYS 201: force and energy.
We we will go a little bit further and develop
two more concepts that are related to force
and energy: electric field and voltage.
With the idea of voltage we will look at the
flow of electricity in basic electric circuits.
Force - Review of Gravity
We have already considered one of the basic
forces in nature: gravity.
Newton’s Law of gravity said that every mass
attracts every other mass according to the
relation:
Fgravity = G M1 m2 / r122 (attractive)
(We also had Weight = Fgravity = mg but that
was special for the earth’s surface.)
Electric Force and Charge
It took a lot longer, but we finally realized that
there is an Electric Force that is basic and
works in a similar way. But the force
wasn’t between the mass of two objects.
Instead, we found that there was another
property associated with matter: charge.
But unlike gravity where the force was
ONLY ATTRACTIVE, we find that the
electric force is sometimes attractive but
also sometimes REPULSIVE.
Electric Charge
In order to account for both attractive and
repulsive forces and describe electricity
fully, we needed to have two different kinds
of charge, which we call positive and
negative.
Gravity with only attractive forces needed
only one kind of mass. Electricity, with
attractive and repulsive forces, needs two
kinds of charge.
Electric Force
To account for repulsive and attractive
charges, we found that like charges repel,
and unlike charges attract.
We also found that the force decreases with
distance between the charges just like
gravity, so we have Coulomb’s Law:
Felectricity = k q1 q2 / r122 where k, like G in
gravity, describes the strength of the force
in terms of the units used.
Electric Force
Charge is a fundamental quantity, like
length, mass and time. The unit of charge
in the MKS system is called the Coulomb.
When charges are in Coulombs, forces in
Newtons, and distances in meters, the
Coulomb constant, k, has the value:
k = 9.0 x 109 Nt*m2 / Coul2 . (Compare this
to G which is 6.67 x 10-11 Nt*m2 / kg2 !)
Electric Force
The big value of k compared to G indicates
that electricity is VERY STRONG
compared to gravity. Of course, we know
that getting hit by lightning is a BIG DEAL!
But how can electricity be so strong, and
yet normally we don’t realize it’s there in
the way we do gravity?
Electric Force
The answer comes from the fact that, while
gravity is only attractive, electricity can be
attractive AND repulsive.
Since positive and negative charges tend to attract,
they will tend to come together and cancel one
another out. If a third charge is in the area of the
two that have come together, it will be attracted to
one, but repulsed from the other. If the first two
charges are equal, the attraction and repulsion on
the third will balance out, just as if the charges
weren’t there!
Fundamental Charges
When we break matter up, we find there are
just a few fundamental particles: electron,
proton and neutron. (We’ll consider whether
these three are really fundamental or not in the last part of
this course, and whether there are any more fundamental
particles in addition to these three.)
electron: qe = -1.6 x 10-19 Coul; me = 9.1 x 10-31 kg
proton: qp = +1.6 x 10-19 Coul; mp = 1.67 x 10-27 kg
neutron: qn = 0;
mn = 1.67 x 10-27 kg
(note: despite what appears above, the mass of neutron and
proton are NOT exactly the same; the neutron is slightly
heavier; however, the charge of the proton and electron
ARE exactly the same - except for sign)
Fundamental Charges
Note that the electron and proton both have
the same charge, with the electron being
negative and the proton being positive. This
amount of charge is often called the
electronic charge, e. This electronic
charge is generally considered a positive
value (just like g in gravity). We add the
negative sign when we need to:
qe = -e; qp = +e.
Electric Forces
Unlike gravity, where we usually have one big
mass (such as the earth) in order to have a
gravitational force worth considering, in
electricity we often have lots of charges
distributed around that are deserving of our
attention!
This leads to a concept that can aid us in
considering many charges: the concept of
Electric Field.
Concept of “Field”
How does the electric force (or the
gravitational force, for that matter), cause a
force across a distance of space?
In the case of gravity, are there “little devils”
that lasso you and pull you down when you
jump? Do professional athletes “pay off the
devils” so that they can jump higher?
Answer: We can develop a better theory than this!
Electric Field
One way to explain this “action at a distance”
is this: each charge sets up a “field” in
space, and this “field” then acts on any
other charges that go through the space.
One supporting piece of evidence for this idea
is: if you wiggle a charge, the force on a
second charge should also wiggle. Does
this second charge feel the wiggle in the
force instantaneously, or does it take a little
time?
Electric Field
What we find is that it does take a little time
for the information about the “wiggle” to
get to the other charge. (It travels at the
speed of light, so it is extremely fast, but not
instantaneous!)
This is the basic idea behind radio
communication: we wiggle charges at the
radio station, and your radio picks up the
“wiggles” and decodes them to give you the
information.
Gravitational Field
We already started with this idea of field in
gravity, although we probably didn’t
identify the field concept as such:
Weight = Fgravity = mg
where we have g = GM/r2 .
This little g we called the acceleration due to
gravity, but we also call it the gravitational
field due to the big M.
Electric Field
The field strength should depend on the
charge or charges that set it up. The force
depends on the field set up by those charges
and the amount of charge of the particle at
that point in space (in the field):
Fon 2 = q2 * Efrom 1 (like Fgr = m*g)
or, Efrom 1 = Fon 2 / q2 .
Note that since F is a vector and q is a scalar,
E must be a vector.
Electric Field for a point charge
If I have just one point charge setting up the
field, and a second point charge comes into
the field, I know (from Coulomb’s Law)
that
Fon 2 = k q1 q2 / r122
and
Fon 2 = q2 * Eat 2
which gives:
E at 2 due to 1 = k q1 / r122 for a point charge.
Inverse Square Law
E from1 = k q1 / r122 for a point charge, and
g = G M / r2 for a mass. Why do both have
an inverse square of distance (1/r2) ?
If we consider that the field consists of a
bunch of “moving particles” that make up
the field, the density of particles, and hence
the strength of the field, will decrease as
they spread out over a larger area (A=4pr2).
[The 4p is incorporated into the constants k and G.]
Inverse Square Law
As the “field particles” go away from the source,
they get further away from each other – they
become less dense and so the field is weaker.
Electric Force - example
What is the electric force on a 3 Coulomb
charge due to a -5 Coulomb charge located
7 cm to the right of the 3 Coulomb charge?
What is the electric field due to the -5
Coulomb charge at the location where the 3
Coulomb charge is?
7 cm
+3 Coul.
-5 Coul
Electric Force - example
From Coulomb’s Law, we know that there is
an electric force between any two charges:
F = kq1q2/r122 , with the direction determined
by the signs of the charges.
F = (9x109 Nt-m2/C2) * (3 C) * (5 C) / (.07 m)2 =
2.76 x 1013 Nt. Note that we ignore the sign on
any charge when calculating the magnitude.
Since the charges are opposite, the force is
attractive!
7 cm
+3 Coul.
-5 Coul
Electric Force - example
F = 2.76 x 1013 Nt.
Note that this force is huge: over 27 trillion
Newtons which is equivalent to the weight
of about 6 billion tons! What this indicates
is that it is extremely hard to separate
coulombs of charges. Most of the time, we
can only separate picoCoulombs or
nanoCoulombs of charge.
Electric Field - example
The Electric Field can be found two different ways.
1. Since we know the electric force and the charge
at the field point, we can use: F = qE, or
Eat 1 = F/q1 = 2.76 x 1013 Nt / 3 C = 9.18 x 1012 Nt/C.
Since the charge at the field point is positive, the
force and field point in the same direction.
2. Since we are dealing with the field due to a point
charge (the -5 C charge), we can use:
Eat 1 = kq/r2 = (9x109Nt-m2/C2) * (5 C) / (.07m)2 =
9.18 x 1012 Nt/C; since the charge causing the field
is negative, the field points towards the charge.
+3 Coul.
7 cm
-5 Coul
Another Force Example
Suppose that we have an electron orbiting a
proton such that the radius of the electron in
its circular orbit is 1 x 10-10m (this is one of
the excited states of hydrogen). How fast
will the electron be going in its orbit?
qproton = +e = 1.6 x 10-19 Coul
qelectron = -e = -1.6 x 10-19 Coul
p
r = 1 x 10-10 m,
r
melectron = 9.1 x 10-31kg
v
e
Force Example
Why is this labeled a “Force” example instead of an energy example? Energy is
generally easier to use since it doesn’t
involve direction or time.
v
p
r
e
Force Example
To use the Conservation of Energy example,
we need to have a change from one form of
energy into another form. But in circular
motion, the distance (and hence potential
energy) stays the same, and the electron will
orbit in a circular orbit at a constant
velocity, so the kinetic energy does not
change. Therefore, there is no transfer of
energy and the Conservation of Energy
method will not give us any information!
Force Example
We first recognize this as a circular motion
problem and a Newton’s Second Law
problem where the electric force causes the
circular motion:
S F = ma where Fcenter = Felec = k e e / r2
directed towards the center, m is the mass
of the electron since the electron is the
particle that is moving, and
acirc = w2r = v2/r.
Force Example
SF = ma becomes ke2/r2 = m(v2/r), or
v = [ke2/mr]1/2 =
[{9x109 * (1.6x10-19)2} / {9.1x10-31 * 1x10-10}]1/2 =
1.59 x 106 m/s (or 3.5 million miles per hour).
Note that we took the + and - signs for the charges
into account when we determined that the electric
force was attractive and directed towards the
center. The magnitude has to be considered as
positive.
Finding Electric Fields
We can calculate the electric field in space
due to any number of charges in space by
simply adding together the many individual
Electric fields due to the point charges!
(See Computer Homework, Vol 3 #1 & #2 for examples.
These programs are NOT required for this course, but you
may want to look at the Introductions and see how to work
these types of problems. If you simply type in guesses, the
computer will show you how to work the problems.)
Finding Electric Fields
In the first laboratory experiment,
Simulation of Electric Fields, we use a
computer to perform the many vector
additions required to look at the electric
field due to several charges in several
geometries.
With the calculus, we can even determine the
electric fields due to certain continuous
distributions of charges, such as charges on
a wire or a plate.
Electrical Energies
Just as Newton’s Laws worked completely,
but were difficult, so to, working with
Electric Forces will be difficult.
Just as with gravitation, in electricity we can
solve many problems using the
Conservation of Energy, a scalar equation
that does not involve time or direction. This
requires that we find an expression for the
electric energy.
Electric Potential Energy
Since Coulomb’s Law has the same form as
Newton’s Law of Gravity, we will get a
very similar formula for electric potential
energy:
PEel = k q1 q2 / r12
Recall for gravity, PEgr = - G m1 m2 / r12 .
Note that the PEelectric does NOT have a
minus sign. This is because two like
charges repel instead of attract as in gravity.
Voltage
Just like we did with forces on particles to get
fields in space,
(Eat 2 due to 1 = Fon 2/ q2)
we can define an electric voltage in space (a
scalar):
Vat 2 due to 1 = PEof 2 / q2 .
We often use this definition this way:
PEof 2 = q2 * Vat 2 .
Units
The unit for voltage is, from the definition:
Vat 2 = PEof 2 / q2
volt = Joule / Coulomb .
Note that voltage, like field, exists in space,
while energy, like force, is associated with a
particle!
Gravitational Analogy
In electricity we have: PEof 2 = q2 * Vat 2 .
In gravity (as you may recall) we have:
PE = m * g * h .
As you can see, charge is like mass, and
voltage is like the combination (g*h). We
can think of a high voltage as similar to
either a big height where gravity is constant,
or as a given height on a planet with very
strong gravity.
Gravitational Analogy
In electricity we have: PEof 2 = q2 * Vat 2 .
In gravity (as you may recall) we have:
PE = m * g * h .
In gravity it takes both a mass and a height to
have potential energy.
In electricity it takes both a charge and a
voltage to have potential energy. A high
voltage with only a small amount of charge
contains only a fairly small amount of energy.
Different batteries what is different?
1. What is the difference between a 9 volt
battery and a AAA battery?
2. What is the difference between a AAA
battery and a D battery?
3. What is the difference between a 9 volt
battery and a 12 volt car battery? Which is
more dangerous? Why?
Batteries - cont.
1. The 9 volt battery supplies 9 volts. The
AAA battery supplies 1.5 volts.
2. Both the AAA battery and the D battery
supply the same 1.5 volts. Since the D
battery is physically bigger, though, it has
more chemicals in it that can supply more
energy - it can push (lift up) MORE charge
through 1.5 volts than the AAA battery can.
Batteries - cont.
3. Obviously the 9 volt battery has less
voltage than the 12 volt car battery. But
does that make the car battery only 33%
more dangerous?
The car battery is much bigger and so has
MUCH more energy. The car battery can
push lots more charges through the 12 volts
than the 9 volt can push through 9 volts.
Remember that energy is the capacity to do
work, either for good or bad.
Voltage due to a point charge
Since the potential energy of one charge due
to another charge is:
PEel = k q1 q2 / r12
and since voltage is defined to be:
Vat 2 = PEof 2 / q2
we can find a nice formula for the voltage in
space due to a single charge:
Vat 2 due to 1 = k q1 / r12 .
Voltages due to several point
charges
Since voltage, like energy, is a scalar, we can
simply add the voltages created by
individual point charges at any point in
space to find the total voltage at that point
in space:
Vtotal = S k qi / ri .
If we know where the charges are, we can (at
least in principle) determine the voltage at any
location.
Static electricity
Vtotal = S k qi / ri .
Since k is so large (9 x 109 Nt-m2/Coul2), even
a small amount of charge can create very
high voltages. In static electricity (generated
by walking across a rug in the winter), voltages
can become high enough to cause a spark
(when you touch someone else), but with so
little charge going across the high voltage
very little energy (damage) is really done.
Voltages and Electric Fields
Just like force and work are related, so are
field and voltage related:
D PE = W = - F Ds,
so too are electric field and voltage:
D V = - E Ds .
Note that voltage changes only in the
direction of electric field. This also means
that there is no electric field in directions
in which the voltage is constant.
Voltage and Field
D V = - E Ds , or Ex = -DV / Dx .
Note also the minus sign means that electric
field goes from high voltage towards low
voltage.
Note also that this means that
positive charges will tend to “fall” from
high voltage to low voltage (like masses tend
to fall from high places to low places) , but that
negative charges will tend to “rise” from
low voltage to high voltage (like bubbles
tend to rise) !
Voltage and Field
D V = - E Ds , or Ex = -DV / Dx .
Note that the units of electric field are (from its
definition: E = F/q) Nt/Coul.
But from the above relation, they are
equivalently Volts/m.
Hence: Nt/Coul = Volt/m.
Voltage, Field and Energy
The Computer Homework, Vol 3, #3, has an
introduction and problems concerning these
ideas that relate voltage to field
D V = - E Ds
and voltage to energy
PEof 2 = q2 * Vat 2
for use with the Conservation of Energy Law.
Review
F1on2 = k q1 q2 / r122 PE12 = k q1 q2 / r12
Fon 2 = q2 Eat 2
PEof 2 = q2 Vat 2
Eat 2 = k q1 / r122
Vat 2 = k q1 / r12
use in
use in
S F = ma
KEi + PEi = KEf +PEf +Elost
VECTOR
scalar
Ex = -DV / Dx
Energy example
Through how many volts will a proton have to
be accelerated if it is to reach a million
miles per hour?
DV = ?
qproton = 1.6 x 10-19 Coul
mproton = 1.67 x 10-27 kg
vi = 0 m/s
vf = 1 x 106 mph * (1 m/s / 2.24 mph) =
4.46x105 m/s .
Energy Example
Since Volts are asked for, and voltage is connected to
potential energy, this suggests we use
Conservation of Energy.
We can use the Conservation of Energy including
the formulas for kinetic energy and potential
energy:
KEi + PEi = KEf + PEf + Elost , where
KE = (1/2)mv2 and PE = qV:
(1/2)mpvi2 + qpVi = (1/2)mpvf2 + qpVf + Elost
Since vi=0 and Elost=0, and bringing qpVf to the left
side, we have: qp(Vi-Vf) = (1/2)mpvf2.
Energy Example
qp(Vi-Vf) = (1/2)mpvf2
We note that (Vi-Vf) = -DV since the change
is normally final minus initial. Thus,
DV = -(1/2)mpvf2 / qp =
-(1/2)(1.67x10-27)(4.46x105)2 / 1.6x10-19 =
-1040 volts.
We see that the proton must fall down (DV is
negative) through 1040 volts to reach a
million miles/hour.
Voltage, Force and Energy
The second assigned computer homework,
Vol 3, #4, on Electric Deflection, provides
a problem involving energy (PE = qV) and
force (F = qE, where Ey = -DV/Dy ).
[NOTE: You only need to get 6/10 on this program
to get full credit.]
The situation in this program is what occurs in
a TV or computer monitor.