Chapter 21
Electric Charge
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
“Dangerous, therefore, is it to
take shelter under a tree, during
a thunder-gust. It has been fatal
to many, both men and beasts."
- Benjamin Franklin
David J. Starling
Penn State Hazleton
PHYS 212
Coulomb’s Law
Examples
Electric Charge
Objectives
(a) Describe basic aspects of electric charge: positive,
negative, neutral, the charge of subatomic particles,
conductors, insulators, discharging charged objects,
grounding, conservation of charge, quantization of
charge.
(b) Predict the motion of charges on conductors and
insulators, particularly when charges are added
to/removed from the object, or charged objects are
moved relative to the object.
(c) Employ Coulomb’s Law (including the shell rules) to
calculate the electric force (both magnitude and
direction) between point charges and/or uniform shells
or spheres of charge, and be able to compare the forces
in different situations.
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Review
Chapter 21
Electric Charge
Review
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Pre-requisite: Mechanics (PHYS 211)
Electric Charge
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We learned all about the contributions of Newton:
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
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Position: ~r(t), Velocity: ~v(t) and Acceleration: ~a(t)
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Forces: ~Fnet = m~a
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Momentum: ~P = m~v
Chapter 21
Electric Charge
Review
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~
Angular position: θ(t),
Angular velocity: ω
~ (t) and
Review
Electric Charge
Angular acceleration: α
~ (t)
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Angular momentum: ~L = ~r × ~p or L = Iω
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Torque: ~τ = ~r × ~F, ~τnet = I~
α
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Work: W = ~F · ~d
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Kinetic Energy: K = 12 mv2
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Potential Energy:
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
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Gravitational: Ug = mgh
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Gravitational, large distances: UG = − Gmr1 m2
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Spring: Us = 12 kx2
Conservation Laws:
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energy
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momentum and angular momentum
Electric Charge
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
From gizmodo.com, by Bertrand Kulik
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What is lightning?
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Lightning is the motion of electric charge through the
air.
Electric Charge
Chapter 21
Electric Charge
Review
Electric Charge
What is charge?
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A proton has one unit of positive charge
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An electron has one unit of negative charge
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A neutron is charge-free
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The charge on an electron (or proton) is −1.6 × 10−19
C (+1.6 × 10−19 C)
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The unit of charge is the coulomb, named after
Charles-Augustin de Coulomb.
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Electric Charge
Chapter 21
Electric Charge
Review
Electric Charge
Why do two charged glass rods push each other away?
(a) An evil spirit possesses the rods.
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
(b) They contain opposite charges, and opposite charges
repel.
(c) They contain the same charge, and like charges repel.
(d) The rods polarize each other, redistributing the charge,
which causes them to repel.
Electric Charge
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Glass rods hold “positive” charge
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Plastic rods hold “negative” charge
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Metallic rods can hold either
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Electric Charge
Chapter 21
Electric Charge
Review
The truth about charge:
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Opposites attract: positive and negative charges pull on
each other, like gravity
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Like charges repel: negative and negative or positive
and positive push each other away
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The size of the charge matters: the bigger the charge,
the bigger the force
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Charge and mass are unrelated; a large object may have
a small charge, and a small object may have a large
charge.
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Charge is Quantized
Chapter 21
Electric Charge
Review
Electric Charge
Charge comes in packets of ±e (one proton/electron
Charge is Quantized and
Conserved
charge).
Conductor vs. Insulator
Coulomb’s Law
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An electron has charge −e
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A proton has charge +e
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A neutron has charge 0
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Most matter is made of these three constituents
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(Inside of protons and neutrons there are quarks, which
have charges 23 e and − 13 e)
Examples
Charge is Quantized
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Charge is Quantized
Chapter 21
Electric Charge
Review
Charge is not a “substance” like water or food; it is a
property of an object!
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Consider the following phrases:
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“Charge on a sphere”
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“Charge transferred”
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“Amount of charge”
The charge is counted/transferred by counting/transferring
the particles that have the property “charge.”
Examples
Charge is Conserved
Chapter 21
Electric Charge
Review
Electric Charge
We see all sorts of reactions in experiments, converting one
species to another. But in each, charge is conserved.
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Here are some examples:
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γ → e+ + e− (pair production)
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e+ + e− → γ + γ (annihilation)
I 238 U
→
234 Th
+ 4 He (radioactive decay)
Conductor vs. Insulator
Conductors and Insulators
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Conductor: a material through which charge can move
freely
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Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Insulator: a material through which charge does not
Coulomb’s Law
move
Examples
Semiconductors: a material that can be a conductor or
an insulator, depending on the situation (At least 1
Nobel Prize, 1956)
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Chapter 21
Electric Charge
Superconductor: a material that conducts charge
perfectly, with no resistance (5 Nobel Prizes, as recent
as 2003)
What makes a material one or the other?
Conduction Electrons!
Conductor vs. Insulator
Chapter 21
Electric Charge
Review
Charge is free to move on a conductor, so it moves around
when a charged object is nearby:
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Conductor vs. Insulator
Chapter 21
Electric Charge
Review
Electric Charge
What happens if you bring a charged glass rod (positive!)
near a neutral copper rod?
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
(a) The rods attract (just like before)
(b) The rods repel (opposite of before)
(c) Nothing happens to the rods
(d) Not enough information
Coulomb’s Law
How do we determine the forces involved in charge
interactions? Let’s first define some variables:
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
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Charge is q
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The distance between two objects 1 and 2 is r12
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The unit vector, pointing to charge 1 from charge 2 is
Coulomb’s Law
Examples
r̂12 (so ~r12 = r12 r̂12 ).
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We also need to know the universal constant:
0 = 8.85 × 10−12 F/m called the vacuum
permittivity or electric constant.
Chapter 21
Electric Charge
Coulomb’s Law
Review
Consider two “point charges”:
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
The force on charge 1 from charge 2 is just:
~F12 = k q1 q2 r̂12
2
r12
where k = 1/4π0 .
(1)
Chapter 21
Electric Charge
Coulomb’s Law
If you replace k with G, and the q’s with m’s, we have
gravity:
~F12 = G m1 m2 r̂12
(2)
2
r12
In fact, just like with gravity, these forces obey the principle
of superposition:
~Fnet = ~F12 + ~F13 + ~F14 + ... + ~F1n
This is the force on charged particle 1 from all the other
charged particles nearby.
(3)
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Example 1
Two positively charged particles sit on the x-axis a distance
r = 0.020 m apart. The charges are q1 = 1.60 × 10−19 C
and q2 = 3.20 × 10−19 C. What is the magnitude of the
force exerted on charge 1 from charge 2?
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Example 2
Chapter 21
Electric Charge
Review
Electric Charge
Now we add a third charged particle between the two, a
distance 34 r from particle 1. The new particle has the same
charge as particle 2, but negative: q3 = −3.20 × 10−19 C.
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Is the net force on particle 1 to the left or the right?
(a) Left
(b) Right
(c) Can’t tell from information given
Example 2
Now we add a third charged particle between the two, a
distance 34 r from particle 1. The new particle has a charge of
q3 = −3.20 × 10−19 C.
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
What is the new electrostatic force on particle 1 from the
other two?
Example 3
Chapter 21
Electric Charge
Review
Electric Charge
Let us now move particle three off the x-axis and call it
particle 4. It is still a distance 34 r from particle 1, but on a
line that makes an angle of 60◦ from the x-axis.
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
In what general direction is the net force on particle 1?
(a) Upper plane (I and II)
(b) Lower plane (III and IV)
(c) Fifth quadrant
(d) Not enough information
Example 3
Let us now move particle three off the x-axis and call it
particle 4. It is still a distance 34 r from particle 1, but on a
line that makes an angle of 60◦ from the x-axis.
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
What is the new electrostatic force on particle 1 from the
other two?
Example 4
Chapter 21
Electric Charge
Review
Two particles lie on the x-axis a distance L apart (with 1 at
the origin). Their charges are q1 = 8q and q2 = −2q (q is
unknown). At what location can a proton be placed such
that it is in equilibrium?
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Where do we have to put the proton so that the forces can be
balanced?
(a) On the left
(b) In the middle
(c) On the right
(d) Not enough information
Example 4
Two particles lie on the x-axis a distance L apart (with 1 at
the origin). Their charges are q1 = 8q and q2 = −2q (q is
unknown). At what location can a proton be placed such
that it is in equilibrium?
Chapter 21
Electric Charge
Review
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
Example 5
Chapter 21
Electric Charge
Review
When two conductors are electrically connected, the total
charge is shared between them. If the two conductors are
identical, the charge is evenly distributed.
Electric Charge
Charge is Quantized and
Conserved
Conductor vs. Insulator
Coulomb’s Law
Examples
The ground is like an infinite conductor, making anything
connected to it “neutral” or “uncharged.”