Download Ch. 19: Electric charges, Forces, and Fields (Dr. Andrei Galiautdinov, UGA)

Ch. 19: Electric charges, Forces, and Fields
(Dr. Andrei Galiautdinov, UGA)
2014FALL - PHYS1112
Paper & comb demo…

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The most basic electrical phenomenon…
static electricity
• The silk handkerchief exhibits a static cling to a cotton shirt in the
dryer.
• The door knob provides a shock after scuffing your feet on the
carpet.
• Sparks fly when you pull the wool sweater off.
• A lightning strikes during a storm.
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Girl with a balloon…
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Hair…up in the air
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What do you think happened here?
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What do you think happened here?
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An important person in the history of the
human kind…
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…was the balloon rubbed on Donald’s hair?
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…was the balloon rubbed on Donald’s hair?
unlikely…
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…my guess is, these are
polarization charges
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Two balloons…
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Were they charged by rubbing against each other?
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Both balloons are NEGATIVELY charged
(must have been charged separately)
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Kids on playground slides…
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Plastic playground slides create enough
static to fry hearing implants!
Most kids have no problem with the static electricity
created from sliding down plastic slides. For
children with cochlear implants it's more
complicated, though.
The static can shut down the cochlear implant
instantly. Cochlear implants were first introduced in
the 1980s and have always had problems with static
electricity.
In the beginning, they could be shut down by simply
putting on a sweater. Now they are more stable, but
they can still shut down with static from slides and
balloons.
When the cochlear implant is shut down it costs
$1,000 to be restored. It can also take days to get it
done, leaving the child deaf for days.
A company in Missouri that is developing anti-static
coating for the Navy is seeing if their product will
work on slides. They believe that they could produce
it for slides at an affordable price. Metal slides aren’t
terribly helpful even though they don’t produce
static, because they get too hot to slide down in
warm weather.
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Lightning
we’ll discuss this later, after introducing the notion of the electric field and
the phenomenon of air breakdown
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A bit of history…
ancient Greeks:
William Gilbert:
1.
2.
Electrification is not limited
to amber; it’s a general
phenomenon
Amber (by wool) + feather
Magnetite (Fe2O3) + iron
- 700
0
Charles Dufay (King of
France’s gardener):
1733
1600
Hans Oersted:
Michael Faraday:
Inverse-square force
law for electricity
Connection b/w electricity
and magnetism (compass
needle is deflected by
current)
1.
2.
Heinrich Hertz:
Produced EM waves
in the lab
1887
Concept of E & M fields
EM Induction (changing
magnetic field produces
current in a circuit)
1831
1820
Alexander Popov
Joseph Thomson:
Guglielmo Marconi:
Discovery of the
Radio
electron
1896
1. + and – electricity
2. Likes repel,
opposites attract
Electrically charged objects
can also repel each other
Charles Coulomb:
1785
Benjamin Franklin:
1897
1750
James Clerk Maxwell:
1. Laws of E&M in
modern form
2. Existence of EM
waves
3. Light is an EM
wave
1865 to 1873
P. N. Lebedev:
E. Rutherford:
Niels Bohr:
Light pressure
“planetary”
model of atom
“(semi-)
quantum” model
of atom
1900
1911
1913
Charles-Augustin de Coulomb (14 June
1736 – 23 August 1806) was a French
physicist.
He is best known for developing
Coulomb's law (the inverse-square law
of electrostatics).
The SI unit of electric charge, the
coulomb, was named after him.
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Unit of charge
Name: coulomb [C]
Definition (different from the technical SI definition):
1 [C] = charge of (6.242 x 1018) protons = (6.242 x 1018 ) qp,
where qp is the basic atomic unit of charge.
Thus,
qp = 1.602 x 10-19 [C]
Note: electron charge is qe = (- qp) = - 1.602 x 10-19 [C]
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Coulomb’s Law
Coulomb’s law gives the force between two point charges:
The force is along the line connecting the charges, and is
attractive if the charges are opposite, and repulsive if the charges
are like.
Coulomb’s Law
The forces on the two charges are action-reaction forces.
Superposition principle
If there are multiple point charges, the forces add by superposition.
1 [C] is a huge amount of charge. Here’s an example:
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1 [C] is a huge amount of charge. Here’s an example:
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The Field Concept
(took 2,500 years to arrive at)
A bit of history…
ancient Greeks:
William Gilbert:
1.
2.
Electrification is not limited
to amber; it’s a general
phenomenon
Amber (by wool) + feather
Magnetite (Fe2O3) + iron
- 700
0
Charles Dufay (King of
France’s gardener):
1733
1600
Hans Oersted:
Michael Faraday:
Inverse-square force
law for electricity
Connection b/w electricity
and magnetism (compass
needle is deflected by
current)
1.
2.
Heinrich Hertz:
Produced EM waves
in the lab
1887
Concept of E & M fields
EM Induction (changing
magnetic field produces
current in a circuit)
1831
1820
Alexander Popov
Joseph Thomson:
Guglielmo Marconi:
Discovery of the
Radio
electron
1896
1. + and – electricity
2. Likes repel,
opposites attract
Electrically charged objects
can also repel each other
Charles Coulomb:
1785
Benjamin Franklin:
1897
1750
James Clerk Maxwell:
1. Laws of E&M in
modern form
2. Existence of EM
waves
3. Light is an EM
wave
1865 to 1873
P. N. Lebedev:
E. Rutherford:
Niels Bohr:
Light pressure
“planetary”
model of atom
“(semi-)
quantum” model
of atom
1900
1911
1913
Michael Faraday (22 September 1791 – 25
August 1867), one of the most influential
scientists in history.
Discoveries include:
•
•
•
•
•
•
Michael Faraday, 1842
The concept of the electromagnetic field
Faraday's law of electromagnetic induction
Electrochemistry (Faraday's laws of
electrolysis; Faraday constant)
Chemistry (discovered benzene, invented
an early form of the Bunsen burner and the
system of oxidation numbers, and
popularized terminology such as anode,
cathode, electrode, and ion.)
Faraday effect (magnetic field causes a
rotation of the plane of polarization of light
- the first experimental evidence that light
and electromagnetism are related)
Faraday wheel (which formed the
foundation of electric motor technology.)
The SI unit of capacitance, the farad, is named
in his honor.
+1 +6 -2
H2SO4
Albert Einstein kept a picture of Faraday on
his study wall, alongside pictures of Isaac
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Newton and James Clerk Maxwell.
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The Field Concept (1)
1)
Taken literally, Coulomb’s Law describes an Action-at-a-Distance Model of
electrostatic interactions in which charges (charged particles) exert forces
directly and instantaneously on one another across the distance separating
them.
Note: these forces act along the lines connecting the charges
Symbolically: charge  charge
2) This model is good when charges are at rest.
3) Problems arise when charges are allowed to move.
Example:
- Charge 1 on Earth, charge 2 on Moon.
- If charge 1 wiggles (for whatever reason), charge 2 (according to
Coulomb) would immediately experience a different force.
- This doesn’t seem right!
- This leads to violation of STR, according to which no influence can
propagate faster than the speed of light.
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The Field Concept (2)
1)
The Field Model instead imagines that a charge particle creates a field in the
space around it, and another particle responds to the field at its own location,
not to the first particle directly.
Symbolically: charge  field  charge
2) How does this resolve the problem of moving charges?
In our previous example:
- When charge 1 is wiggled, it does not directly affect the distant charge 2.
- Rather, the wiggling particle wiggles the values of the field in its
immediate vicinity.
- These wiggles in turn affect the field values at slightly more distant
locations, and so on.
- The net effect is that ripples in the field move away from the wiggling particle at a
finite speed (similar to how ripples on the surface of water do; the difference is, the
ripples in the field do not need any medium to propagate in, so they can propagate
in a vacuum).
- As a result, only when the ripples reach the distant charged particle will it feel a
wiggling force.
The Field Concept (3)
1)
A field, (unlike a particle) exists not at a specific location but throughout
space.
2) Even so, the field is a physical object (entity) that (like a particle) has energy,
carries momentum, and obeys its own equations of motion.
3) We need a field model b/c instantaneous action at a distance violates STR (no
signal can propagate faster than the speed of light). The Field Model naturally
resolves this problem.
4) Mathematically, we describe a field (formally) by assigning some kind of
numerical quantity to every point in space at every moment in time – in our
case, vectors.
5) Physically, we define the field (operationally) in terms of what it does – in our
case, in terms of forces it exerts on charged particles.
The Field Concept (4)
1)
So, physically, we define the field (operationally) in terms of what it does – in
our case, in terms of forces it exerts on charged particles.
2)
Here’s how it works:
- +
+ -- -+
+-+-+
+
+-
P
Bring in qtest and
hold it at rest;
then measure the
force on it.
3) Then, by definition:
Distribution of charge
(regarded as the source of
the field at point P).
Charges in this distribution
are allowed to move
arbitrarily.


Fe
E≡
qtest
By definition:
The Field Concept (5)


Fe
E≡
qtest
Translation:
a)
This eq. defines the E-field vector at a point in space & time.
b) Fe is the electrostatic force experienced at that time by a small test particle with charge qtest held
at rest at that point in space.
c)
qtest must be small, so that the force it exerts on the charges in the distribution does not push
around the charges whose field we are trying to measure.
d) E-vector points in the same direction as Fe if qtest is positive.
e)
Why divide Fe by qtest? – B/c it is found experimentally that, no matter how source charges move,
the force Fe the test charge experiences at a given location is proportional to qtest itself. So,
dividing by qtest produces a quantity E that depends only on position relative to the charges
creating the field and not on the magnitude of the test charge qtest we use.
f)
Why keep qtest at rest? – B/c if qtest moves (has non-zero velocity) it will experience an additional
force (magnetic force) due to motion of the source charges.
By definition:
Note:
The Field Concept (6)


Fe
E≡
qtest
E-field is a vector quantity, but it is important to remember that it consists of an infinite
number of vectors attached to every point in space at any moment in time.
To describe the E-field fully you must specify E-vectors everywhere.
Unit: [E] = N/C
Examples:
1. On a sunny day, due to various atmospheric processes that separate charges,
E = 100 to 150 (N/C)
2. During a thunderstorm, E > 10,000 (N/C)
3. When taking a shower, by moving water, E ~ 800 (N/C)
4. In dry air, if E > 3,000,000 (N/C), the air breaks and becomes a conductor, sparks fly.
The Field Concept (7)
Once the E-field has been determined, we can find the
force it exerts on any charged particle by:


Fe = qE (any charge; limitations apply)
Note:
Fe
E
(if q > 0)
Fe
E
(if q < 0)
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(magnitude)
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Electric field lines.
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Electric dipole.
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Approx. value; found
without a calculator.
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The following is not needed in our class.
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Gauss’ Law
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Gauss’ Law
(concepts)
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E2
E1
All of these guesses are wrong!
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E1
E2
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Gauss’ Law
(extra slides from previous semester; not really
needed)
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A voltaic pile (~1800) on
display in the Tempio
Voltiano.
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More slides from previous semester
(not really needed)
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The End
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