ELEC 1206 Electrical
Materials and Fields
Electric Charge & Coulombs Law
Dr. Grace Chai
Grace Chai
 Joined Southampton in Jan 2015 as a lecturer in
EFY
 Moved to ECS in Sept 2016
 Optoelectronics Research Centre (ORC) - research
 USMC academic office (R4013)
 Email: grace.chai@soton.ac.uk
 Contact hours: Email for appointment
2
Research
• Infrared thermography analysis using convolution neural
network
• Semiconductor devices characterization using advanced
spectroscopic techniques – temperature dependent PL, PR
• Optical properties of ZnO, carbon- doped ZnO
• Optical properties of Laser-induced graphene
• SiGe gas sensors
3
Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
5
Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
6
Electrical Materials & Fields
7
Electrical Materials & Fields
next few weeks:
• Electro-magnetism :Electricity
– Electric Charge and Coulomb's Law.
– Electric Field and Gauss Law.
– Electric Potential and Capacitance.
– Current, Resistance, and Circuits
Halliday Resnick Walker, Part 3 Chapter 21-33,
but for now only 21,22,24,25,26
Electric Charge &
Coulombs Law

Charge




Origin
Quantization
Conservation
Halliday Resnick Walker, Chapter 21
Electro-magnetic Force

Coulombs Law




Properties
SI Units
Principle of Superposition
Some calculations
Origin of Charge
• atom
– Nucleus
• Radius: 0.00001 nm
• proton: positive charge
• neutrons: neutral
• 1.6724×10-27 kg /particle
– Electrons
• negative electric charge
• Orbiting (0.1 nm)
• 9.1083×10-31 kg /electron
e=1.60x10-19 C
Some history…
600 BC
William Gilbert demonstrating his
experiments to Queen Elizabeth.
electricity is from the Greek word for amber (elektron)
13
Some history…
14
Charge Quantization
• electrons and proton have equal and opposite charge: e
• quantized
– Millikan experiment (1910)
– no fractional charge
– Q=ne
– e=1.602×10-19 Coulomb
1 Coulomb = 1 Ampere-second C=As
Millikan experiment
When the oil drop is in the electric field, there is an electric force, F,
acting upwards. This is given by:
F = Eq where q is the charge on the oil drop
and E is the field strength.
= Vq/d where V is the voltage on the plates
and d is their separation.
The drop is being pulled down by its weight, mg. When the drop is
suspended and stationary, the net force is zero. So:
Vq/d–mg=0
Vq/d=mg
q = mgd/V
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Millikan experiment
• To find the weight of the drop, Millikan let it fall through the air
and measured its terminal velocity. At this point, the net force is
zero – i.e. weight is balanced by the viscous drag. The viscous
drag, D, is given by:
• D = 6πηvr where η is the viscosity of air, r is the radius of a
spherical drop and v is its speed.
This allowed him to work out the radius of the drop and
therefore its weight.
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Millikan experiment
•
To find the weight of the drop, Millikan let it fall through the air and measured its terminal velocity. At
this point, the net force is zero – i.e. weight is balanced by the viscous drag. The viscous drag, D, is
given by:
•
D = 6πηvr where η is the viscosity of air, r is the radius of a spherical drop and v is its speed.
This allowed him to work out the radius of the drop and therefore its weight.
•
Having measured the charge on a number of oil drops, q1, q2, q3, etc, Millikan reasoned that each
charge must be a whole number multiple of the fundamental charge, e. So:
q1,= n1e, q2,= n2e, q3,= n3e and so on, where n is a whole number in each case.
So he found e by finding the highest common factor of all the values of charge that he measured on the
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oil drops.
Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
21
Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
22
Charge Conservation
• charge is conserved......
– we cannot create or destroy a single electron
• but we can create combinations of positive and negative:
• radio-active decay:
n→p+e
14C(6p,
8n, 6e) → N(7p,7n,7e)
– if we put a positive charge somewhere, we have automatically put a
negative charge somewhere else
• and created a capacitor by doing so!
Electric Charge &
Coulombs Law

Charge




Origin
Quantization
Conservation
Halliday Resnick Walker, Chapter 21
Electro-magnetic Force

Coulombs Law




Properties
SI Units
Principle of Superposition
Some calculations
Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
25
Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
26
4 Fundamental Forces
• Strong nuclear force
– “Proton-proton interaction”
• Weak nuclear force
– “neutron to proton decay”
• Gravitation
– Planetary motion
– Things dropping
• Electro-magnetic force
– Everything else !!
Coulomb’s law

q1q2
F = k 2
r
• Charles Coulomb 1785
• q= charge of a “particle”
• r=distance between particles
• k= electrostatic constant
Analogy with gravitation
q1q2
F =k 2
r
m1m2
F =G 2
r
• proportional to charge/mass
• proportional to inverse of distance squared
• force parallel to the line joining charges
attractive or repulsive
SI units (systeme internationale)
q1q2
F =k 2
r
1
q1q2
F=
2
4πε 0 r
• cgs electrostatic units [cm,gram,s]
– F [dyne], q [esu], r [cm], k=1
• SI units [m,kg,s]
– F [Newton], q [C], r [m], k= 8.99×109 Nm2C-2
– k=1/4πε0 with ε0 : permittivity of vacuum
– ε0 =8.85 ×10-12 N-1m-2C2
• dimensional analysis!
Superposition of point charges
• resultant force on a charge equals the sum of the
individual forces exerted by all other charges
• vector algebra





F0 = F01 + F02 + F03 + F0 n
• Forces might also be due to gravitation
Example 1
• Three positive charges lie along the same line, find the
force on charge Q2.
Q1
a
Q2
b
Q3
• According to Coulomb’s law, the force on Q2 from left to
right is given by
Q3Q2
Q1Q2
Q2 Q1 Q3
( 2 − 2)
F=
−
=
2
2
4πε 0 a
4πε 0b
4πε 0 a
b
Example 2
• Three equal charges locate at the corners
of a triangle. Find the force on the charge
Q at A
• There are two forces on A with a
magnitude of
Q2
F=
4πε 0 a 2
Q
a
a
• The resultant force on A is
2
2
Q
3
Q
=
F = 2 cos 300
2
4πε 0 a
4πε 0 a 2
A
B
Q
a
Q
C
how much is a Coulomb?
•
2 table tennis balls charged to 1 Coulomb 50 cm apart
4 seconds
– 60 Watt lamp for ....
1C
• same charges repel 2nd ball upwards
• gravitational force needed to compensate ?
A: force of ball 2.5g
C: midsize car 1000kg
B: 3 pints of beer 2kg
D: Eiffel tower 10kton
50cm
1C
E: 10 empire state buildings 3.60Mton
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Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
36
Learning Outcomes
At the end of this lecture, you will be able to:
• describe the electrical properties of the particles inside an
atom
• identify that the net charge in an isolated physical process
cannot be changed (conservation of charge)
• draw a free body diagram to show the electrostatic force on it
and anchoring the tail of the force vector on that particle
• relate the magnitude of the electrostatic force, the charge
magnitudes of the particles and the separation between the
particles in pairs
• calculate the net force acting on a particle
37
Tutorial
Question 1
Identical isolated conducting spheres 1 and 2 have equal charges
and are separated by a distance that is large compared with their
diameters (Fig a). The electrostatic force acting on sphere 2 due to
⃗
sphere 1 is 𝐹𝐹.
Suppose now that a third identical
sphere 3 having an insulating handle
and initially neutral, is touched first
to sphere 1 Fig b, then to sphere 2 Fig
c. and finally removed (Fig d). The
electrostatic force that now acts on
sphere 2 has magnitude F’. What is
the ratio F’/F.
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Question 2
A particle of charge +3.00×10−6C is 12.0cm distant from a
second particle of charge −1.50×10−6C. Calculate the
magnitude of the electrostatic force between the particles.
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Question 3
In the figure below, particle of charge +1.0µC and particle 2 of
charge -3.0µC are held at separation L=10.0cm on an x-axis. If
particle 3 of unknown charge q3 is to be located such that the
net electrostatic force on it from particles 1 and 2 is zero, what
must be the (a) x and (b) y coordinates of particles 3?
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Question 4
A nonconducting spherical shell, with an inner radius of
4.0cm and an outer radius of 6.0cm, has charge spread
nonuniformly through its volume between its inner and outer
surfaces. The volume charge density 𝜌𝜌 is the charge per unit
volume, with the unit coulomb per cubic meter. For this shell r
𝜌𝜌 = 𝑏𝑏/𝑟𝑟, where r is the distance in meters from the center of
the shell and b 𝑏𝑏 = 3.0𝜇𝜇𝜇𝜇/𝑚𝑚2 . What is the net charge in the
shell?
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Question 5
In the figure shown, particles 1 and 2 of
charge 𝑞𝑞1 = 𝑞𝑞2 = +3.20𝑥𝑥10−19 𝐶𝐶 are on
a y-axis at distance 𝑑𝑑 = 17.0𝑐𝑐𝑐𝑐 from the
origin. Particle 3 of charge 𝑞𝑞3 =
+ 6.40𝑥𝑥10−19 𝐶𝐶 is moved gradually along
the x axis from 𝑥𝑥 = 0 to 𝑥𝑥 = +5.0𝑚𝑚.
At what values of x will the magnitude
of the electrostatic force on the third
particle from the other two particles be
(a) minimum and
(b) maximum?
What are the (c) minimum and
(d) maximum magnitudes?
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