Electric fields arise from electric charges and can be represented by electric field lines. A positive test charge experiences a force when placed in an electric field, allowing the field strength to be calculated. The field is strongest closest to the charged object and decreases with distance. Materials are classified as conductors, insulators or semiconductors based on how easily their electrons can move. Coulomb's law defines the force between two point charges as directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

1. Topic 5: Electricity &
Magnetism
Topic 5.1
Electric Fields

2. Electric Field & Force
 What do you know about electric forces?
 What does an electric field look like?
 What experience have you had with
electric fields?
 How is electricity generated?

3. Electrification by Friction
Electric charge, or `electricity', can come from batteries and
generators. But some materials become charged when they
are rubbed. Their charge is sometimes called electrostatic
charge or `static electricity'. It causes sparks and crackles
when you take off a pullover, and if you slide out of a car
seat and touch the door, it may even give you a shock.

4. Two Types of Charge
Polythene and Perspex can be charged by
rubbing them with a dry, woollen cloth.
When two charged polythene rods are
brought close together, they repel (try to
push each other apart).
The same thing happens with two charged
Perspex rods.

7. However, a charged polythene rod and a
charged Perspex rod attract each other.
Experiments like this suggest that there are
two different and opposite types of electric
charge.
These are called positive (+) charge and
negative (-) charge:

8. Conservation of Charge
Where charges come from
Everything is made of tiny particles called
atoms. These have electric charge inside
them.
There is a central nucleus made up of
protons and neutrons. Orbiting the nucleus
are much lighter electrons.
We quantify charge using the unit
“Coulombs”, C.

9. Electrons have a negative (-) charge.
Protons have an equal positive (+) charge.
Neutrons have no charge.

10. Normally, atoms have equal numbers of
electrons and protons, so the net (overall)
charge on a material is zero.
However, when two materials are rubbed
together, electrons may be transferred
from one to the other.
One material ends up with more electrons
than normal and the other with less.
So one has a net negative charge, while
the other is left with a net positive charge.

11. Rubbing materials together does not make
electric charge. It just separates charges
that are already there.
Charge is always conserved in any action,
the distribution of charge is changed.

12. Question
 If a million electrons are transferred in one
rub by a cloth, what are the resulting
charges in Coulombs of
(i) 3 rubs of polythene
(ii) 5 rubs of Perspex
(iii) the rods from (i) and (ii) are made to
touch

13. Materials
When some materials gain charge, they lose
it almost immediately. This is because
electrons flow through them or the
surrounding material until the balance of
negative and positive charge is restored.

14. Conductors
Conductors are materials that let electrons
pass through them. Metals are the best
electrical conductors.
Some of their electrons are so loosely held
to their atoms that they can pass freely
between them.These free electrons also
make metals good thermal conductors.
Most non-metals conduct charge poorly or
not at all, although carbon (in the form of
graphite) is an exception.

15. Insulators
Insulators are materials that hardly conduct
at all. Their electrons are tightly held to
atoms and are not free to move - although
they can be transferred by rubbing.
Insulators are easy to charge by rubbing
because any electrons that get transferred
tend to stay where they are.

16. Semiconductors
Semiconductors are `in-between'
materials.
They are poor conductors when cold, but
much better conductors when warm.
Eg, silicon or germanium

17. Electrostatic Induction
Attraction of uncharged
objects
A charged object will
attract any uncharged
object close to it. For
example, the charged
screen of a TV will attract
dust.

18. The previous diagram shows what
happens if a positively charged rod is
brought near a small piece of aluminium
foil.
Electrons in the foil are pulled towards the
rod, which leaves the bottom of the foil
with a net positive charge.
As a result, the top of the foil is attracted
to the rod, while the bottom is repelled.
However, the attraction is stronger
because the attracting charges are closer
than the repelling ones.

20. Electroscope
In 1786 the Rev. Abraham
Bennet introduced a device
called a ‘gold leaf
electroscope’.
It consists of two extremely thin
gold leaves hanging parallel to
each other connected to a
conducting stem and cap.The
internal system is protected
from air currents by a glass
enclosure.

21. Electroscope
The outer case and stand
system is separated from the
inner system by an insulating
plug.
At PAC we use a needle
electrometer where the needle
replaces the easily damaged
gold leaf.

22. Using an Electroscope
An electroscope can be charged positively
by induction with a negative rod

23. Using an Electroscope
The electroscope can test the sign of a
charge.
The electroscope is first charged positively
-by stroking the cap with a strongly + ively
charged glass rod or
-by induction using a -ively charged
ebonite rod.

24. Using an Electroscope
The object whose charge is to be tested is
slowly brought near to the cap of the
electroscope.
If the rod is uncharged, then the charged
electroscope will induce a charge on it, and
since the nearer side of the rod is negatively
charged.

25. Using an Electroscope
In effect the rod will behave as a negatively
charged one, and repel electrons to the
needle, neutralising positive charge and
decreasing needle divergence.

26. Using an Electroscope
It is easy to distinguish a + ively charged
electroscope.

27. Using an Electroscope
To tell the difference between a neutrally
charged rod and a negatively charged rod,
we need to earth the electroscope.
An uncharged rod will cause no deflection
while the negatively charged rod will cause
the needle to diverge.
Repulsion is the only sure test for
determining the sign of a charge.

28. Coulomb’s Law
The force between two point
charges is directly proportional to
the product of the charges and
inversely proportional to their
distance apart squared.
+1 +3
r

29. Equations
F  q1 q2 / r2
Or F = k q1 q2 / r2
Where k = 1/4πε0
ε0 is the permittivity of free space
Therefore Coulomb’s Law can be written as
F = q1 q2 / 4πε0r2

30. Applying Coulomb’s Law
To determine the net force on a charge due
to two or more other charges, you must use
vector addition.
Find the force and direction due to each of
the other charges in turn and then resolve
these forces to get the resultant force.

31. Coulomb’s Law
Coulomb’s law states that the force acting
between two charges q1 and q2 whose
distances are separated by a distance d is
directly proportional to the product of the
charges and inversely proportional to the
square of the distance between them. The
force is along the line joining the centres of
the charges.

32. Coulomb’s Law
𝑭 =
𝟏
𝟒𝝅𝜺𝜺 𝒐
𝒒 𝟏 𝒒 𝟐
𝒓 𝟐

33. Question 1
1. Find the force when
(a) 2 protons are placed 1.00 mm apart
(b) proton and electron are placed
1.00 x 10-9m apart
(c) helium nuclei and an electron are
1.00 x 10-6m apart

34. Q1 (a) Solution
𝐹 =
1
4𝜋𝜀 𝑜
𝑞1 𝑞1
𝑟2
𝐹 = 8.99 x 109
1.6 x 10−19
x1.6 x 10−19
(1 x 10−3) 2
F = 2.30 x 10−22
N repulsion

35. Q1 (b) Solution
𝐹 =
1
4𝜋𝜀 𝑜
𝑞1 𝑞1
𝑟2
𝐹 = 8.99 x 109
1.6 x 10−19
x1.6 x 10−19
(1 x 10−9) 2
F = 2.30 x 10−10
N attraction

36. Q1 (c) Solution
𝐹 =
1
4𝜋𝜀 𝑜
𝑞1 𝑞1
𝑟2
𝐹 = 8.99 x 109
3.2 x 10−19
x1.6 x 10−19
(1 x 10−6) 2
F = 4.60 x 10−16
N attraction

37. Question 2
2. Find the force acting on a +10.0 C charge
placed 60.0 cm east of a +6.00 C charge and
40.0 cm north of a -8.00 C charge.

38. Q 2 Solution
q2 = -8.00 μ C
q = +10.0 μ C
q1 = +6.00 μ C
60 x 10-2 m
40 x 10-2 m

39. Q 2 Solution
𝐹𝑞𝑞1 =
1
4𝜋𝜀 𝑜
𝑞𝑞1
𝑟2
𝐹𝑞𝑞1 = 8.99 x 109
10 x 10−6
x 8 x 10−6
(60 x 10−2) 2
𝐹𝑞𝑞1 = 1.49833333 N East
Don’t round yet

40. Q 2 Solution
𝐹𝑞𝑞2 =
1
4𝜋𝜀 𝑜
𝑞𝑞2
𝑟2
𝐹𝑞𝑞2 = 8.99 x 109
10 x 10−6
x 8 x 10−6
(40 x 10−2) 2
𝐹𝑞𝑞2 = 4.495 N South
Don’t round yet

41. Q 2 Solution
q2 = -8.00 μ C
q = +10.0 μ C
q1 = +6.00 μ C
60 x 10-2 m
1.49833333 N
4.495 N
Add forces vectorially

42. Q 2 Solution
𝐹 = √(4.495)2 + (1.498333)2
𝐹 = 6.74 N
Direction
Tan θ =
𝑂𝑝
𝐴𝑑𝑗
=
4.495
1.498333
= 3.0000
θ = 71.6o
𝐹 = 6.74 N at 18.4 oT
4.74
4.74

43. Electric Field
A resultant force changes motion. Many
everyday forces are pushes or pulls
between bodies in contact. In other cases
forces arise between bodies that are
separated from one another.
Electric, magnetic and gravitational effects
involve such action-at-a-distance forces and
to deal with them physicists find the idea of
a field of force, or simply a field, useful.

44. Fields of these three types have common features
as well as important differences.
An electric field is a region where an electric
charge experiences a force.
If a very small, positive point charge Q, the test
charge, is placed at any point in an electric field
and it experiences a force F, then the field
strength E (also called the E-field) at that point is
defined by the equation
𝐸 =
𝐹
𝑞

45. The magnitude of E is the force per unit
charge and its direction is that of F (i.e. of
the force which acts on a positive charge).
Field strength E is thus a vector.
If F is in newtons (N) and Q is in
coulombs (C) then the unit of E is the
newton per coulomb (N C-1).
A more common but equivalent unit is the
volt per metre (V m-1).

46. To determine the net field strength on a
charge due to two or more other charges,
we must use vector addition.
Find the field strength and direction due to
each of the other charges in turn, and
then resolve these field strengths to get
the resultant field strength.
Remember that the direction of a field is
the direction in which a positive charge
would move .

47. Uniform Electric Field
The field between two parallel plates can be
calculated by

49. Field Patterns
An electric field can be represented and so
visualized by electric field lines.
These are drawn so that
(1) the field line at a point (or the tangent to it if it is
curved) gives the direction of E at that point, i.e.
the direction in which a positive charge would
accelerate,
and (2) the number of lines per unit cross-section
area is proportional to E.
The field line is imaginary but the field it represents
is real.

50. Positive Charge
+

51. A hollow sphere

52. Electric Potential Energy
If you want to move a charge closer to a
charged sphere you have to push against
the repulsive force. You do work and the
charge gains electric potential energy.
If you let go of the charge it will move away
from the sphere, losing electric potential
energy, but gaining kinetic energy.

53. When you move a charge in an electric field
its potential energy changes. This is like
moving a mass in a gravitational field.

54. In the previous figure, a charge +q moves
between points A and B through a
distance x in a uniform electric field.
The positive plate has a high potential
and the negative plate a low potential.
Positive charges of their own accord,
move from a place of high electric
potential to a place of low electric
potential. Electrons move the other way,
from low potential to high potential.

55. In moving from point A to point B in the
diagram, the positive charge +q is moving
from a low electric potential to a high electric
potential.
The electric potential is therefore different at
both points.
In order to move a charge from point A to
point B, a force must be applied to the
charge equal to qE (F = qE).

56. Since the force is applied through a
distance x, then work has to be done to
move the charge, and there is an electric
potential difference between the two
points.
Remember that the work done is
equivalent to the energy gained or lost in
moving the charge through the electric
field.

57. The electric potential V at any point in an
electric field is the potential energy that each
coulomb of positive charge would have if
placed at that point in the field.
The unit for electric potential is the joule per
coulomb (J C-1), or the volt (V).
Like gravitational potential it is a scalar
quantity.

58. Electric Potential Difference
Potential difference
We often need to know the difference in
potential between two points in an electric
field.
The potential difference or p.d. is the energy
transferred when one coulomb of charge
passes from one point to the other point.

59. The diagram shows some values of the
electric potential at points in the electric field
of a positively-charged sphere
What is the p.d. between points A and B in
the diagram?

60. When one coulomb moves from A to B it
gains 15 J of energy.
If 2 C move from A to B then 30 J of energy
are transferred.

61. Change in Energy
Energy transferred,
This could be equal to the amount of electric
potential energy gained or to the amount of
kinetic energy gained
W =charge, q x p.d.., V
(joules) (coulombs) (volts)

62. The Electronvolt
One electron volt (1 eV) is defined as the
energy acquired by an electron as a result of
moving through a potential difference of one
volt.
Since W = q x V and the charge on an
electron or proton is 1.6 x 10-19C
Then, W = 1.6 x 10-19C x 1V
W = 1.6 x 10-19 J
Therefore, 1 eV = 1.6 x 10-19 J

63. Conduction in Metals
A copper wire consists of millions of copper
atoms. Most of the electrons are held tightly
to their atoms, but each copper atom has
one or two electrons which are loosely held.
Since the electrons are negatively charged,
an atom that loses an electron is left with a
positive charge and is called an ion.

65. The diagram shows that the copper wire is
made up of a lattice of positive ions,
surrounded by free' electrons.
The ions can only vibrate about their fixed
positions, but the electrons are free to move
randomly from one ion to another through
the lattice.
All metals have a structure like this.

66. What happens when a battery is
attached to the copper wire?
The free electrons are repelled by the
negative terminal and attracted to the
positive one.
They still have a random movement, but in
addition they all now move slowly in the
same direction through the wire with a
steady drift velocity.
We now have a flow of charge - we have
electric current.

67. Electric Current
Current is measured in amperes (A) using
an ammeter.
The ampere is a fundamental unit.
The ammeter is placed in the circuit so that
the electrons pass through it.Therefore it is
placed in series.
The more electrons that pass through the
ammeter in one second, the higher the
current reading in amps.

68. 1 amp is a flow of about 6 x 1018 electrons in
each second!
The electron is too small to be used as the
basic unit of charge, so instead we use a
much bigger unit called the coulomb (C).
The charge on 1 electron is
only 1.6 x 10-19 C.

69. In fact:
Or I = Δq/ Δt
Current is the rate of flow of charge

70. Which way do the electrons move?
At first, scientists thought that a current was made up
of positive charges moving from positive to negative.
We now know that electrons really flow the opposite
way, but unfortunately the convention has stuck.
Diagrams usually show the direction of `conventional
current' going from positive to negative, but you must
remember that the electrons are really flowing the
opposite way.

71. Drift equation
A metal contains a sea of electrons. These electrons can
move freely. If we consider a unit volume of wire of cross-
sectional area A, then the number of charge carriers can be
found,
If n = number of charge carriers per unit volume
So, charge available = nAdq
where q=charge on a carrier, d = length of wire
Current = q/t
So I = q/t = nAqd/t but, d/t is velocity v
The drift equation becomes, I = n A v q

72. Games
 Check your knowledge of charges & fields
http://phet.colorado.edu/en/simulation/charg
es-and-fields
 Play Electric Field Hockey
http://phet.colorado.edu/en/simulation/electri
c-hockey