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TRANSCRIPT
Electric charge
Coulomb’s law
Electric field
ELECTRICITY Lecture 3.7
ELECTRICITY
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
Interaction between electrically charges objects
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 is a characteristic of sub-atomic particles.
An atom is composed of 3 kinds of particles: protons , electrons and neutrons.
Electric charge and the atom
Simple View
e e
e
Nucleus
Neutrons Protons
Atom
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 -----------------
These particles are, in general, neither created nor destroyed, but electrons can be displaced from one atom to an other.
Electric charge and the atom
Nucleus Carbon Atom
6 protons: charge +6e 6 neutrons: (no charge)
Atoms are electrically neutral -
-
- -
-
-
6 electrons: charge -6e
Electron removed – result positive ion Electron added – result negative ion
Total positive charge of the nucleus
total negative charge of the electrons around the nucleus.
=
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
Balloon and wool rubbed together: balloon becomes negatively charged
Many examples
Plastic comb run through your hair comb will then attract bits of paper
Almost any two non-conducting substances when rubbed together will become 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
•Never fractional charge
•Charge can only have values ±e, ±2e, ±3e ±..
•Charge is said to be quantised
Coulomb’s Law
Charge on an electron = -1.6x10-19C
= 6.25x1018 electrons are required to make up a charge of 1 Coulomb.
-1.6x10-19C
-1C therefore
Example. How many electrons are required to make up a negative charge of one Coulomb?
Fundamental quantity of charge found in matter is that associated with a proton (+e) and electron (-e)
Electric charge
Conductors- •Example: metals, copper etc. •charges are free to move.
Types of Materials
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
+ + q1 q2 F F
r
+ - q1 q2 F F
r
Unlike charges
- - q1 q2 F F
r
Like charges
1 22
q qFr
∝
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.
Charles Coulomb (1736-1806) French physicist,
1 22
q qF kr
=1 22
q qFr
∝
Coulomb’s Law
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)
Coulomb is a very large quantity of charge
The constant k is frequently written as
where ε0 is called the permittivity of free space 0
14
kπε
=
12 2 1 20 8.85 10 C N mε − − −= ×
Coulomb’s Law
Coulomb force is very large compared with gravitational force
Example: Two charges, each of one Coulomb, are a distance of 1 metre apart. What is the force between them?
1 22
0
14
q qFrπε
=1C∗ 1C 4π 8.85x10-12C2N-1m-2 ∗1m∗1m =
F = 9x109 N = 9 billion Newtons
Example Coulomb Force
e0 = 8.85 × 10-12 C2N-1 m-2
mass of an electron = 9.11 × 10-31 kg G = 6.67 × 10-11 N m2 kg-2
Compare electrostatic repulsive force between two electrons held one metre apart in a vacuum and the gravitational force of attraction between them?
Coulomb force
1 22
m mF Gr
=Gravitational force
F = 2.3 x 10-28 N
F = 5.5 x 10-71 N
1 22
0
14
q qFrπε
=
1.6 x10-19C∗ 1.6x10-19C 4π 8.85x10-12C2N-1m-2 ∗1m∗1m
F =
( )211 31
2
6.67 10 9.11 101
F− −× ×
=
Coulomb’s Law
+ - F -F
r Proton q =+e
Electron q= -e
Electron and proton, a distance r apart, are simultaneously released from rest. Where do they collide?
Newton 3rd law, forces are equal and opposite
Collision at midpoint ??
acceleration Newton 2nd law F = ma
a = F m
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
Collide very near initial position of proton
20
12
x v t at= + 212p px a t=
212e ex a t=
e e
p p
x ax a
= //
pe e
p p e
mx F mx F m m
= =
-27
-31
1.67 10 k 18339.11 10 kg 1
e
p
x gx
×= =
×
1833e px x=
+
r
-
Electric Field Electrostatic force and gravitational force can both act through space even when there is no physical contact between the objects involved.
An electric field exists in a region of space around a charged object.
In the case of charged particles, what transmits the force between them?
Gravitational field: g
F = mg
Potential Energy ∆U ≈ mgh
m
mass m experiences a force:
Field lines show the direction of the force and indicate its relative magnitude
Electric field near a negative charge is directed radially into the charge as shown
Electric field near a positive charge is directed radially out from the charge
-
Electric Field
Electric field lines show • direction of the force • indicate its relative magnitude
Similar to gravitational field lines
2+
Electric field lines
Double the charge Double the number of field lines
+
Consider positive test charge q0(fictitious) at A
- A + A +
Electric Field
Consider force on positive test charge
Assume test charge is small and does not affect any other charges
+
q0 q0
Electric field represents the electric force a stationary positive charge experiences.
Test charge: helpful in determining forces generated by other charges
The electric field E is said to exist in the region of space around a charged object.
Example:
Electric Field
+ + +
+ + +
+
+ + + +
+
Q
Electric field E due to charge Q at location of small test charge q0 is given by;
SI unit of electric field
+ q0
Test charge
0
FEq
=
F is the force exerted on q0 by Q
Newton per coulomb (NC-1)
Electric force per Coulomb
Electric Field
02
0
14
QqFrπε
=
20
14
QErπε
=
0Eq=
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
Analogous to F= mg in gravitational field
0
FEq
= 0F q E=
Determine the electric field at A, a distance of 40cm from a positive charge Q of 2x10-3 Coulombs
+ Q
r
A E
Find field E at point A 40 cm from Q.
2
QE kr
=
E= 9 x 109 N.m2C-2 (2 x 10-3) C (0.4m)2
E = 112.5 x106 NC-1
Example
Electric Field
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
Electric charges
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
1 22
q qF kr
=
Coulomb force
420r m
( )9 2 2
2
9 10 0.1 0.1500
Nm C C CN
r
−× ×
( )92 9 10 0.1 0.1
500r
× ×
( )99 10 0.1 0.1500
r× ×
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
Electric charges
Example