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A Course of Physics
A Course of Physics
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GENERAL PHYSICS II
GENERAL PHYSICS II
Electromagnetism
&
Thermal Physics
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CHAPTER VII
CHAPTER VII
Static Electric Field
Static Electric Field
§1. Electric charges. Coulomb’s law
§2. Electric field and electric field vector
§3. Electric flux and Gauss’s law
§4. Electric potential
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It is known that in nature there are four kinds of fundamental
forces which are caused by:
¾ gravitational interaction
¾ electromagnetic interaction (between static or moving
electric charges)
¾ strong interaction (that connects protons and neutrons in
nuclei)
¾ weak interaction (that drives the beta decay)
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We consider now the electromagnetic interaction:
¾ static electric forces between charges

by B. Franklin (1706 – 1790).
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¾ With the modern knowledge about the structure of matter
we know that electric charges come from elementary
particles: negatively charged electron and positively charged
proton. In nuclei there are also neutron with no charge.
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Interaction between charges: two positive charges or two
negative charges repel each other. A positive charge and a
negative charge attract each other. This interaction is called the
static electric interaction.
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Two important principles for charges:
¾ The principle of conservation of charge: “The algebraic sum
of all the electric charges in any closed systeme is constant”
¾ “The magnitude of charge of the electron or proton is a
natural unit of charge”. It is also called the element charge,
that is the smallest charge which cann’t devided into smaller
charges.
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2.2 Coulomb’s law:
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Interaction forces of charges are studied by French
physicsist Charles Augustin de Coulomb (1736 – 1806).
The Coulomb’s law was established in 1785.
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Comparison of electric and gravitational forces:
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More on the concept of FIELD:
¾ Besides the electric field we have known the gravitational
field
¾ Generally, a field is something that can be defined anywhere
in space, it can be represented by a function of 3-D spatial
position f (x, y, z) :
» Temperature field: for each location in space the
temperature has a definite value → T = T (x, y, z).
Temperature is scalar quantity → the temperature field is
a scalar field.
» Force fields, as electric field or gravitational field are
vector fields.
At each point in space,
we define a vector
E = E (x, y, z)
(x,y,z)
E=E(x,y,z)
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2.2 Definition of electric field vector:
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Superposition of electric field:
How can determine the electric field due to a system of many
charges?
We know the principle of superposition of forces: the net force
which exerts on body is the vector sum of all the component
forces
the electric field vector for a system of charges is equal to

Let u = l – x, then
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(b) In this case, the x-components
will cancel out, leaving only
the y-components
dq is as before, and
Express x in terms of θ and integrate