General Physics - PH202 – Winter 2006 – Bjoern Seipel
Electric Charges, Forces and Fields
As reported by the Greek philosopher Thales of Miletus around
600 BC
Greeks found that if they rub an
amber (or “elektron”) rod with
animal fur the rod attract small
light weight objects. They
“charged” the amber rod.
Conclusion:
There is a force between amber
rod and particles!
It is a fundamental force like gravity and called the electric force.
Other combinations of materials like glass and silk are showing the
same effect.
Amber-Amber
Repulsion
Amber – Glas
Attraction
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
1747 Benjamin Franklin
(Besides he helped to draw up the Declaration of Independence)
Defined that there are two kind of charges
(or for a reason that was not recorded)
+ and -
“Opposites attracts”
Like charges repel each other (++ or --)
Unlike charges repel each other (+ -)
Matter consists of
particles that have an
electric charge.
Objects with an equal
amount of both “+
and – particles” have
a zero net charge.
What is charge actually?
Charge is a property of fundamental particles that causes them to
exert forces on each other.
The SI unit of electrical charge is the Coulomb
(more in detail: Electric charge is a conserved property of some subatomic
particles, which determines their electromagnetic interactions. Electrically
charged matter is influenced by, and produces, electromagnetic fields. The
interaction between charge and field is the source of one of the four
fundamental forces, the electromagnetic force.)
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
An example: Atom
Nucleus: Protons and Neutrons
Protons are positive charged
Neutrons have a zero net charge
Electron is negative charged
1 electron + 1 proton (= Hydrogen)
= zero net charge
Relative
charge
Relative
mass
electron
-1
1
1800
proton
+1
1
neutron
o
1
Particle
Representation
Electron mass is 9.11 10-31 kg
Proton mass is 1.6726 10-27 kg
Neutron mass 1,6749 10-27 kg
The electron is a fundamental particle found in nature and is part of
a family of fundamental particles known as leptons
The symbol e is the magnitude of the electron’s charge
The electron charge (-e) is -1.6 ´ 10-19 C.
All electrons have exactly the same charge -e !!!!!!!
The proton and the neutron are not fundamental particles. Each
consists of three quarks.
•The proton charge is (+e) +1.6 ´ 10-19 C.
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
The value of a charge has to be an integer number of
e (+/-e, +/-2e,+/-3e………. )
It can never be a decimal like 1.5e (or in other words the
charge is quantized)
Lets look into the world of quantum mechanics:
Proton and neutron are made of three quarks (so called up and
down quarks, an up quark has a charge of -1/3e and a down quark
of +2/3e).
There are also uncharged fundamental particles such as neutrinos.
Enrico Fermi suggested the name "neutrino" (italien for "little neutral one")
But there is more:
Every particle has an anti-particle. There is an anti-proton, an antineutron and an anti-electron. The anti-electron was the first antiparticle to be detected and we call it the positron. The positron has
exactly the same mass as an electron but a positive charge instead
of a negative one)
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Law of conservation of net charge
The amount of charge produced in any
process is zero
Or in other words:
Charge is just there. You cannot create
nor destroy it but you can separate or
“transfer” it.
Mechanism:
Caused by rubbing the amber rod with
animal fur it transfers electrons from the fur to the rod.
Electrons are at the shell of an atom. They can transferred in most
processes rather than protons
An object is……
Positive charged: Lack of electrons
Negative charged: Surplus of electrons
If the object possesses no net charge it is said to be neutral.
An atom is normally neutral, because it possesses an equal number
of electrons and protons. However, if one or more electrons are
removed or added, an ion is formed, which is charged.
Examples:
1. What is the net charge of a system of 6 protons and 6
electrons?
2. What is the net charge of a system of 8 electrons and 6
protons?
3. How many electrons and protons do the following atoms
have?
• Na
Na+
Cl−
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Why can we pickup/attract light weight with a zero net charge?
That is what we call
“Polarization” of an
object
charged
If bring the positive
charged rod close to
the surface of our
particles nuclei/protons
were repelled,
electrons attracted.
à Elongation of the
surface atoms (Also
called dipole)
neutral & polarized
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Insulators and Conductors
Solid, Liquid, Gas
Materials are classified by how easily charged particles can “flow”
through them. This is measured by the conductivity, a quantity
how freely charge can move in a material. Unit: [Ω-1 – Ohm-1]
Conductivity high: Conductor (i.e. metals)
Conductivity very low: Insulator (i.e. ceramics, plastics)
Only solid
Semiconductor with an intermediate conductivity
Example:
Amber rod, Insulator
Metal sphere, Conductor
Charge is not free to move Charge free to move and distributed
over the surface
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Example: How to charge a metal
sphere positive
1. Electrons were repelled if we
bring the negative charged rod close
to the sphere.
2. We connect sphere with the earth.
Electrons “escape”.
3. Remove connection.
4. Sphere remains positive charged.
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Coulombs Law describe the electric force Fe of
point charges (or spherical charge distributions)
(Coulombs law can applied to all kind of charge distributions with
the appropriate mathematics)
The force is inversely proportional to the square of
the separation of the 2 charges, and is along the line
joining them.
The force is proportional to the product of the
magnitudes of the 2 charges.
Remember force is a vector!
q1 q 2
m1m2
Fe = k
2
2
seems to similar to Fg = G
r12
r12
Electric Force
Gravitational force
The electric force…
…varies directly as the magnitude of each charge
…varies inversely as the square of the distance between charges
…is directed along the line joining the charges
…can be either attractive or repulsive depending on the signs of
the charges
Gravitational field constant G ≈ 7 10-11 N m2 kg-2
Electric field constant
k ≈ 9 109 N m2 C-2
Fe is much stronger than Fg
Fe can be attractive or repulsive; Fg is always attractive
q must be an integer number of e
Comparison between gravitational force and electric
force
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
How much charge is there in 1g H2O
1g H2O ≈ 3.3 x 1022 molecules and each molecule has 18 protons
and 18 electrons.
Also approximately 1024 charges (net charge is still zero!!)
If we would separate 1% of these charges by 1m we there would
be an attractive force of about 5.7 1015N.
Lets be the average weight of a human around 7 103 N.
Example of application of Coulombs Law: Two point charges
If charges at rest
“electrostatic”
Newton’s 3rd Law
F12 = -F21
F21 = k
q1 q 2
2
r12
There may be many charges
around
ð Superposition to find the
resulting force acting on a
point charge
(Principle of Superposition)
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Electric field
Michael Faraday
conceived the concept
of electric field
(force acting over a
distance, it is a concept
of in our minds not of
matter).
The force experienced
by any charge is then viewed as the interaction between the charge
and the electric field.
Electric field vector is equal to the quotient of force vector a
positive point charge q0 (so called test charge) would feel at a
certain point and the test charge itself.
r
r F
E=
q0
The SI unit of electric field is N/C
Why?
E points outward
for a positive
point charge
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
If we know the electric field we can easily calculate the force
acting on a charge in the electric field
r
r
F = qE
ð A positive charge experiences a force in the direction of the
electric field
ð A negative charge in the opposite direction
E points inward
for a negative
point charge
When more charges around
ð Superposition to find
the resulting E-field
acting on a point
charge
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
In order to visualize the electric field in space it is
convenient to draw field lines, which are arrows that
point in the direction of the electric field
If we make the electric field visible with electric field lines. We
need to follow certain rules.
Rules:
Field lines…
ð point always in the direction of E (E is always tangential)
ð start at positive charges or at infinity
ð end at negative charges or at infinity
ð are more dense when E has a greater magnitude
ð the number of field lines entering or leaving a charge is
proportional to the magnitude of the charge
ð field lines always end/start perpendicular to the surface
ð never cross or touch each other
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Examples:
Charged Plate
Field lines parallel to each other
and perpendicular to the surface
Parallel plate capacitor
Two parallel conducting plates
with opposite charge, separated
by a distance d. The electric
field is uniform between the
plates (except at the edges).
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Electric field lines on a conductor
Recall that charges within a conductor are free to
move around easily. If the charges within a conductor
are not in motion, then the system is said to be in
electrostatic equilibrium.
(In a conductor, the charges would move if there was a net force on
them.)
ð charge separation
ð no field inside a conductor (Electrostatic
Shielding)
ð field lines start and end perpendicular
and
field is more dense at a
sharp point of a charged
object
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Electric flux
Is a quantity to calculate the electric “flow” or in other words the
number of field lines through an area A.
We define electric flux F as the value of the electric field
perpendicular to a surface times the area of the surface.
In general,
θ is the angle between the
electric field and the line
perpendicular to the surface
Φ = E A cosθ
Φ=EA
Φ=0
Φ = E A cosθ
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General Physics - PH202 – Winter 2006 – Bjoern Seipel
Example 1:
q
⋅ 4πr 2 = 4π k q
2
r
1
C2
−12
= 8.85 ⋅ 10
ε0 =
4πk
Nm 2
Permitivity of free space
q
⇒ Φ = [Nm 2 / C ] Gauss Law
ε0
Φ = EA = k
ð Charge must be enclosed by the surface, else Φ=0!
Gauss’s Law
Consider an arbitrary surface (Gaussian surface) enclosing a total
charge q. The electric flux through the surface is
q
Φ=
ε0
Flux is
ε0 =
1
4 πk
= 8.85×10 −12 C2 /N ⋅ m2
positive if field lines leave the enclosed volume.
Flux is negative if field lines enter the enclosed volume.
Example 2:
Φ = E (2 A) =
q σA
=
ε0 ε0
σ = ch arg e density
A = surface
σ
⇒E=
2ε 0
ð Electric field independent from distance
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