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Lecture 3.7
ELECTRICITY
Electric charge
Coulomb’s law
Electric field
ELECTRICITY
Interaction between
electrically charges objects
Many important uses
Light
Heat
Rail travel
Computers
Central nervous system
Human body made up of electric charges.
Atoms contain
positive and negative charges
Atoms bound together by electric forces
» molecules
Molecules interact to produce
bones, blood, skin, etc
ELECTRICITY
Historical
6th century B.C., Greeks noticed sparks were
produced when the fossilized tree resin called
amber was rubbed with fur.
Greek word for amber is elektron from which
the word electricity is derived.
Major discovery 1861: Maxwell’s equations.
Unified electric and magnetic phenomena
(electromagnetism).
End of the 19th and early 20th century:
Fundamental discoveries concerning the
electronic structure of the atom were made.
Electric charge and the atom
Electric charge is a characteristic of subatomic particles.
Simple View
An atom is composed of 3 kinds of particles:
protons , electrons and neutrons.
Atom
Nucleus
Neutrons
Protons
e
e
e
Particle
Charge
Value (SI unit)
proton
+e
1.6 x 10-19
Coulomb (C)
electron
-e
-1.6 x 10-19
Coulomb (C)
neutron
none
-----------------
Electric charge and the atom
Carbon Atom
Nucleus
-
6 protons: charge +6e
6 neutrons: (no charge)
-
-
6 electrons: charge -6e
-
Atoms are electrically neutral
Total positive charge
of the nucleus
=
total negative charge
of the electrons
around the nucleus.
These particles are, in general, neither
created nor destroyed, but electrons can
be displaced from one atom to an other.
Electron removed – result  positive ion
Electron added – result  negative ion
Electric charge and the atom
Electric charge is a basic physical property
of subatomic particles, protons and electrons.
3 Properties of charge
1. Two types of charges, positive and negative
2. Charge is conserved.
Cannot be created or destroyed.
Charges can be separated.
3. Like charges repel and unlike changes
attract
Electrostatic forces result from the separation
of positive and negative charges.
Electric charge
Electrically charged materials
Many examples
Almost any two non-conducting substances
when rubbed together will become charged
Plastic comb run through your hair
comb will then attract bits of paper
Balloon and wool rubbed together:
balloon becomes
- negatively charged -- --
+
+
+
+
+
+
-
Friction associated with rubbing does not
create the charge
Charge transferred by movement of electrons
Charge is conserved
Neither created or destroyed
Total amount of charge in universe: constant
Electric charge
Basic unit of positive charge:
+e = 1.6 x 10-19 Coulomb
Basic unit of negative charge:
-e = -1.6 x 10-19 Coulomb (C)
Any charged object:
•Total charge is always a multiple of e
•Charge can only have values ±e, ±2e, ±3e ±..
•Charge is said to be quantised
•Never fractional charge
Coulomb’s Law
Fundamental quantity of charge found in
matter is that associated with
a proton (+e) and electron (-e)
Example. How many electrons are required to
make up a negative charge of one Coulomb?
Charge on an electron = -1.6x10-19C
-1C
therefore -1.6x10-19C
= 6.25x1018 electrons are required to make
up a charge of 1 Coulomb.
Electric charge
Types of Materials
Conductors•Example: metals, copper etc.
•charges are free to move.
Insulators•Example: Rubber, plastic etc
•charges are not free to move.
Semiconductors• Example: Silicon, Germanium
•movement of charges can be controlled by
temperature or doping of the material.
Application: electronic devices
Photoconductors:
•Example:
Selenium
•In darkness:
Insulator
•Exposed to light: conductor
•Application: photocopier, laser printer
Electric charges and forces
Coulomb’s law
Mathematical law that describes how
•like charges repel
•unlike charges attract
Charles Coulomb (1736-1806) French physicist,
Unlike charges
q1
F
+
F -q2
Like charges
q2
q1
F
F
-
r
q1q2
F∝ 2
r
r
q2
F
+
q1
F
+
r
Coulomb’s law: “the force between two point
charges is proportional to the product of
their charge and inversely proportional to
the square of their separation”
Direction of the force: along line joining the
point charges.
Coulomb’s Law
q1q2
F∝ 2
r
q1q2
F =k 2
r
SI unit of charge is called the Coulomb
Force F is known as the Coulomb force or
electrostatic force and its units are Newtons
distance r is in metres
Hence units of k are Nm2C-2
The constant k is determined by experiment to
be 9x109 Nm2C-2 (in a vacuum)
The constant k is frequently written as
k=
1
4πε 0
where ε0 is called the
permittivity of free space
ε 0 8.85 ×10−12 C 2 N −1m −2
=
Coulomb is a very large quantity of charge
Coulomb’s Law
Example: Two charges, each of one Coulomb,
are a distance of 1 metre apart. What is the
force between them?
1C∗ 1C
1 q1q2
F=
2 = 4π 8.85x10-12C2N-1m-2 ∗1m∗1m
4πε 0 r
F = 9x109 N = 9 billion Newtons
Coulomb force is very large
compared with gravitational force
Coulomb Force
Example
Compare electrostatic repulsive force between
two electrons held one metre apart in a vacuum
and the gravitational force of attraction between
them? e = 8.85 × 10-12 C2N-1 m-2
0
mass of an electron = 9.11 × 10-31 kg
G = 6.67 × 10-11 N m2 kg-2
1 q1q2
F=
4πε 0 r 2
Coulomb force
1.6 x10-19C∗ 1.6x10-19C
F=
4π 8.85x10-12C2N-1m-2 ∗1m∗1m
F = 2.3 x 10-28 N
Gravitational force
F=
6.67 ×10
−11
m1m2
F =G 2
r
( 9.11×10 )
−31 2
12
F = 5.5 x 10-71 N
Coulomb’s Law
Electron and proton, a distance r apart, are
simultaneously released from rest. Where do
they collide?
-F + F
Proton
q =+e
r
Electron
q= -e
Newton 3rd law, forces are equal and opposite
Collision at midpoint ??
acceleration
F
a= m
Newton 2nd law F = ma
electron mass = 9.11 × 10-31 kg
proton mass = 1.67 × 10-27 kg
Mass of proton ≈ 1833 times mass of electron
acceleration of electron 1833 times greater
Coulomb’s Law
1 2
=
x v0t + at
2
xe ae
=
xp ap
xe
xp
1 2
xe = aet
2
1 2
x p = a pt
2
xe F / me m p
= =
x p F / m p me
1.67 ×10-27 kg 1833
=
-31
9.11×10 kg
1
xe = 1833 x p
+ r
Collide very near initial position of proton
Electric Field
Electrostatic force and gravitational force can
both act through space even when there is no
physical contact between the objects involved.
Gravitational field: g
m
mass m experiences
a force: F = mg
Potential Energy
∆U ≈ mgh
Field lines show the direction
of the force and indicate its relative magnitude
In the case of charged particles, what transmits
the force between them?
An electric field exists in a region of space
around a charged object.
Electric Field
Electric field lines
+
-
Electric field near a
negative charge is
directed radially into
the charge as shown
2+
Electric field near a
positive charge is
directed radially out
from the charge
Double the charge
Double the number
of field lines
Similar to gravitational field lines
Electric field lines show
• direction of the force
• indicate its relative magnitude
Electric Field
Consider positive test charge q0(fictitious) at A
Test charge:
helpful in determining forces generated by
other charges
Assume test charge is small and does
not affect any other charges
Consider force on positive test charge
q0
+A
-
q0
+A
+
Electric field represents the electric force a
stationary positive charge experiences.
Electric Field
The electric field E is said to exist in the region
of space around a charged object.
Example:
Q
+++ +
+ +++
+ ++
+
Test charge
q0
+
F is the force exerted on q0 by Q
Electric field E due to charge Q at
location of small test charge q0 is given by;
F
E=
q0
Electric force per Coulomb
SI unit of electric field
Newton per coulomb (NC-1)
Electric Field
F
E=
q0
F = q0 E
Analogous to
F= mg in gravitational field
 1  Qq0
F =
 2
 4πε 0  r
= Eq0
 1 Q
E =
 2
 4πε 0  r
Electric field at a given point depends only on
the charge Q on the object setting up the field
and the distance r from the object to the specific
point in space
Electric Field
Example
Determine the electric field at A, a
distance of 40cm from a positive charge Q
of 2x10-3 Coulombs
Q
A E
+
r
Find field E at point A
40 cm from Q.
Q
E=k 2
r
-3) C
(2
x
10
E= 9 x 109 N.m2C-2
(0.4m)2
E = 112.5 x106 NC-1
Electric charges
Example
How many electrons must be removed from
an object so that it is left with a charge
of 8 x10-10 C
Total charge = 8 x 10-10 C
Charge on electron = -1.6 x 10-19 C
Therefore number of electrons removed
=
8 x 10-10 C
1.6 x 10-19 C
= 5 x 109 electrons
Coulomb force
Example
Determine the minimum distance apart two
identical charges of 0.1 C must be in order that
the Coulomb force between them is less
than 500 N. k = (9 x 109) Nm2C-2
q1q2
F =k 2
r
9 ×109 Nm 2C −2 ( 0.1C × 0.1C )
500 N 
r2
9
9
×
10
0.1× 0.1)
(
2
r 
500
9 ×109 ( 0.1× 0.1)
r
500
r  420m
Electric charges
Example
An object has a total charge of -2 x10-6 C.
How many excess electrons does the
object have.
Total charge = -2 x 10-6 C
Charge on electron = -1.6 x 10-19 C
Therefore number of excess electrons
=
-2 x 10-6 C
-1.6 x 10-19 C
= 1.25 x 1013 electrons