Videos
SP212
Vector Intro
http://youtu.be/A05n32Bl0aY
Semolina seeds in oil
http://www.youtube.com/watch?v=7vnmL853784
Bending Water with Charges
http://youtu.be/xHrgXDM3jAg
Demonstration: Balloons bending water, repulsion,
attraction, etc.
Demonstration: Spinning rod.
Ch. 21 - Electric Charge
Maj Jeremy Best USMC
Physics Department, U.S. Naval Academy
January 15, 2016
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Electric Charge
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Electric Charge
Electric Charge is an intrinsic property of many of the
fundamental particles that make up everyday matter.
Electric charge comes in two varieties, Positive (+) and
Negative (−)
Like charges repel each other
Opposite charges attract each other
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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The labels “Positive” and “Negative” are
historically arbitrary, and could have been
anything.
Figure: http://www.xkcd.com/567/
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Conductors and Insulators
Coulomb’s Law
The electrostatic force between two charged particles is
described by Coulomb’s Law:
At this stage, we will discuss two classes of material:
Conductors and Insulators
Conductors are materials in which charges are free
to move around .
Insulators are materials in which charges are fixed
in place.
The most common charged particles we will discuss are
Protons (+) and electrons (−) .
It is the electrons in a material that are free to move
around.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
5 / 24
Coulomb’s Law
q - The charges on the two particles.
r - The distance between the two particles
r̂r - A unit vector pointing from one particle to the other.
Its only job is to point.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Charge
The SI unit of charge is the coulomb (C) . For practical
reasons (measurement accuracy), it is defined in terms of
the ampere (A), the unit of current. This will be covered
in more detail in Chapter 26. For now, current and
charge are related by:
Electrostatic Constant
k - The electrostatic constant
k=
~F = k |q1 ||q2 | r̂r
r2
1
= 8.99 × 109 Nm2 /C2
4π0
i=
0 - The permittivity of free space.
dq
dt
0 = 8.85 × 10−12 C2 /Nm2
1(C ) = 1(A) · 1(s)
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
8 / 24
Coulomb’s Law - The Revenge
Problem: Coulomb’s Law
Two particles are fixed on the x-axis. The charges on the
particles are q1 = 1.60 × 10−19 C and
q2 = 3.20 × 10−19 C. The particles are separated by
R = 0.0200 m. What are the magnitude and direction of
the force on particle 1 due to particle 2 (F12 )?
The electrostatic force between two charged particles is
described by Coulomb’s Law:
~F = k |q1 ||q2 | r̂r
r2
Look familiar (think Physics I)?
~F = G m1 m2 r̂r
r2
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Solution:
Both particles are the same sign, so the force is directed
away from particle 2 . Its magnitude is given by
Coulomb’s Law:
1 |q1 ||q2 |
4π0 R 2
F12 = (8.99 × 109 ) Nm2 /C2 ×
(1.6 × 10−19 C)(3.20 × 10−19 C)
(0.0200 m)2
F12 = 1.15 × 10−24 N
or ~F12 = −(1.15 × 10−24 N) ı̂
F12 =
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Coulomb’s Law (again)
Problem: But WAIT, theres MORE!! (Charges)
Now we add a third particle, of charge
q3 = −3.20 × 10−19 C at a distance 34 R from q1 . What is
the net force on particle 1 now?
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Solution:
Coulomb’s Law handles F13 :
Solution:
F13 =
1 |q1 ||q3 |
4π0 ( 34 R)2
−24
F13 = 2.05 × 10
~F1,net = ~F12 + ~F13
= −1.15 × 10−24 N + 2.05 × 10−24 N
N
= (9.00 × 10−25 N) ı̂
Because q3 is negatively charged, its force on q1 is
attractive, and the net force on q1 is, as always, the
vector sum of all the forces acting on it:
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Quantization of Charge
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Quantization of Charge
Charge, like military ranks, is quantized. It only comes
in discrete chunks, without intermediate values (there are
no MIDN 3.4/C).
Water is also a good example.
All charges are integer multiples of the elementary
charge, e:
The charge on an electron is: −e
The charge on a proton is: +e
The charge on a neutron is: 0
e = 1.602 × 10−19 C
q = ne, n = ±1, ±2, ±3, ...
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Charge
Many phrases used regarding charge make it sound
like a substance.
1
2
3
The charge on a sphere.
The amount of charge transferred.
Charge carried by an electron.
These phrases refer to NET (total) charge.
Charge is a property of particles!
Particles have mass and charge, among other things
used to describe them.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Charge, like momentum, and energy is conserved.
Charge removed from one place must be added to
another, it cannot disappear.
This principle is very important in the analysis of nuclear
reactions. Uranium naturally decays:
q2
F =
4π0 r 2
where q is the magnitude of charge on each drop
and r is the center-to-center separation.
If N is the number of excess electrons then:
q
N =−
e
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Conservation of Charge
Solution:
1
The magnitude of the force is given by:
2
Problem: Charged Water
Two tiny, spherical water drops, with identical charges,
of −1.00 × 10−16 C, have a center-to-center separation
of 1.00 cm.
1
What is the magnitude of the electrostatic force
acting between them?
2
How many excess electrons are on each drop, giving
the charge imbalance?
January 15, 2016
238
U
92
→ 234
Th + 42 He
90
e+ + e− → γ + γ
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Problem: Go Nuclear...
To clearly show that charge is conserved, we will do
some charge balancing in nuclear reactions:
Remember AtomicMass
Element
Protons
1
Solution:
1
H
1
+ 94 Be → 95 B + 10 n
H + 9 Be → X + n
12
C
6
12
C + 1H → X
15
N
7
15
+ 11 H → 137 N
+ 11 H → 42 He + 126 C
N + 1 H → 4 He + X
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
January 15, 2016
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
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Additional Sample Problems
Wiley Plus Homework
Chapter 21:
Questions: 2, 7.
Problems: 7, 15, 27, 42
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Problem:
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212