Electrostatics - Coulomb’s Law
Dr Miguel Cavero
July 22, 2014
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Classical Physics
The three main branches of classical physics are Mechanics, Thermal
Physics and Electromagnetism.
The first part of this module concerns electrostatics (charges at rest).
Electrical current is simply the rate of flow of charge over time.
Electrical current is the source of magnetism.
Electrostatics
Introduction
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Fundamental Forces
Recall the four fundamental forces:
strong nuclear force
electromagnetic force
weak nuclear force
gravitational force (or simply, gravity)
Only considered gravity with any detail.
Gravity is the weakest of the four fundamental forces.
Electrostatics
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Forces And Mass
The force due to gravity between any two masses m1 and m2 is given
by
Gm1 m2
F=
r̂
r2
Here, F is the force by m1 on m2 , G is the universal gravitational
constant and r̂ is the unit vector pointing from mass m1 to mass m2 .
This is an example of an inverse-square law.
Gravity is (always) an attractive force.
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Forces And Mass
The magnitude of the gravitational force between masses m1 and m2 is
F =
Electrostatics
Gm1 m2
r2
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Forces And Mass
Newton’s Second Law says that a net force on a mass results in an
acceleration.
F = ma
Another way of looking at this, in terms of gravity, is that a mass in a
gravitational field experiences a gravitational force (the weight).
W = mg
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Charges At Rest
As gravity is a force that resulting from the interaction of objects with
mass, the electromagnetic force results from the interaction of particles
that have a property called electric charge.
Electric charge is a property that is as fundamental as mass.
The atom is made up of protons, neutrons and electrons.
Protons and electrons have charge associated with them, while the
neutron does not.
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Electrostatics
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Properties Of The Electric Charge
The properties of (electric) charges are as follows:
1 There are two types of electric charge: positive and negative.
2 Charge is conserved: the principle of charge conservation states
that the algebraic sum of all charges in a closed system is
conserved.
3 Charge is quantized: the magnitude is always an integer multiple
of the basic unit of charge.
4 Charge is invariant: the charge of a particle is independent of its
speed.
5 Two stationary, point charges interact via the electrostatic force
which is given by Coulomb’s Law.
Electrostatics
Electrostatics
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Coulomb’s Law
The force between any two, stationary point charges, q1 and q2 , is:
proportional to the product of their charges
inversely proportional to the square of the distance between them
The magnitude of the electrostatic force, F , is
F ∝
|q1 ||q2 |
r2
where r is the distance between q1 and q2 (|q1 | is the magnitude of the
charge q1 ).
The electrostatic force is directed along the line joining q1 and q2 .
The force is attractive if the charges are of opposite sign, and repulsive
if the charges have the same sign.
Electrostatics
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Coulomb’s Law
In vector form, Coulomb’s Law is
F12 = ke
q1 q2
r̂12
r2
where F12 is the force exerted by q1 on q2 , and r̂12 is the unit vector
which points from q1 to q2 .
The proportionality constant ke is
ke =
1
≈ 9.0 × 109 N m2 C−2
4πε0
The SI unit of charge is the Coulomb, C.
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Electrostatics
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Coulomb’s Law
The electrostatic force between two charges of opposite sign is
F12 = ke
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q1 q2
r̂12
r2
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Coulomb’s Law
The electrostatic force between two charges of equal sign is
F12 = ke
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q1 q2
r̂12
r2
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Example 1
Point charges of 2 µC and −3 µC are at rest 4 cm apart in a vacuum.
Calculate the force on the 2 µC charge.
First, draw a diagram.
Second, calculate the magnitude of the electrostatic force.
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Example 1
Point charges of 2 µC and −3 µC are at rest 4 cm apart in a vacuum.
Calculate the force on the 2 µC charge.
The magnitude of the electrostatic force on the 2 µC charge is
F
= ke
|q1 ||q2 |
r2
= (9.0 × 109 )
(2 × 10−6 ) × (3 × 10−6 )
(0.04)2
= 33.8 N
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Example 1
Point charges of 2 µC and −3 µC are at rest 4 cm apart in a vacuum.
Calculate the force on the 2 µC charge.
Finally, what is the direction of the force on he 2 µC charge?
The force is attractive, and therefore points towards the −3 µC charge.
Electrostatics
Electrostatics
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Electrostatic Force And Gravity
An electron has mass 9.11 × 10−31 kg and charge −1.60 × 10−19 C.
A proton has mass 1.67 × 10−27 kg and charge +1.60 × 10−19 C.
The magnitude of the gravitational force of attraction between the
proton and electron at a distance of 10 × 10−10 m is
Fg ≈ 1.01 × 10−49 N
The magnitude of the electrostatic force of attraction between the
proton and electron at the same distance of 10 × 10−10 m is
Fe ≈ 2.30 × 10−10 N
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