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Grade 11
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SESSION 9: ELECTROSTATICS
Key Concepts
In this session we will focus on summarising what you need to know about:
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Electrostatics and types of charges
Electric fields, properties and strength
Conservation of Charge
Coulomb’s Law of Electrostatics
Electrical potential energy & potential difference
Electrical potential difference
X-planation
ELECTROSTATICS
There are two types of charges:
 Positive – when a substance has lost electrons.
 Negative – when a substance has gained electrons.
ELECTRIC FIELDS
An electric field is a region in space in which an electric charge will experience a
force.
It is represented by a pattern of field lines. An electric field line is a line drawn in such
a way that at any point on the line, a small positive point charge placed at that point
will experience a force in the direction of the tangent of the line.
CONSERVATION OF CHARGE
The Law of Conservation of Charge states that charges cannot be created nor
destroyed, but are merely transferred from one object to another, i.e. the amount of
charges in a closed system remains the same.
According to the law, when two charged spheres of the same size are brought into
contact, electrons move from the more negative sphere to the less negative sphere
till the charge is spread evenly over both spheres. On separation, each sphere
carries half the total charge of the two spheres.
COULOMB’S LAW OF ELECTROSTATICS
The law states that the force of attraction or repulsion between the two electric
charges at rest is directly proportional to the product of the charges and inversely
proportional to the square of the distance between them.
kQ1 Q 2
F 
r2
Q = charge, unit: coulomb (C)
r = distance between the charges, measured in m
k = Coulomb’s constant = 9 x 109 N.m2.C-2
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UNIT OF CHARGE
CONVERTION TO COULOMB
µC (micro coulomb)
x 10-6
nC (nano coulomb)
x
10-9
pC (pico coulomb)
x
10-12
The charge of an electron is known as an elementary charge (smallest possible
charge).
The charge of an electron is - 1,6 x 10-19 C
The charge of a proton is + 1,6 x 10-19 C
The number of electrons in 1 C of charge is 6,25 x 1018 electrons
ELECTRIC FIELDS
Two charged objects will attract or repel each other without touching – electrostatic
forces are, therefore, non-contact forces and act over a distance.
Definition of an electric field
 an electric field is a region (area) in space where a charge experiences a
force.
 an electric field is not visible.
The direction in which a charge experiences a force can be used to indicate the
electric field pattern.
The field pattern is indicated by electric field lines.
Electric field lines are imaginary lines along which a small positive test charge
would move.
Electric field line properties
1.
2.
3.
4.
5.
6.
Field lines are in the direction indicated by the movement of a small
positive charge (test charge).
Field lines never cross.
Areas where field lines are close together indicate a strong field. The field
is weak where the field lines are far apart.
Field lines begin and end at right angles (perpendicularly) to the charge.
Field lines are continuous.
Field lines are three dimensional.
The field pattern around a positively charged object
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A small positive charge will be repelled by the positively charged object;
therefore the direction of the field is away from the positively charged object.
The field around a single positive charge is not uniform as the field lines are
not parallel.
The field is “stronger” near the charge – the field lines are closer rather than
further apart. There is a greater force on a small positive charge where the
electrostatic field lines are closer together.
The field pattern around a negatively charged object
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The field is not uniform and the direction of the field is towards the charged
object as a small positive charge will be attracted towards the charge.
Resultant field pattern around a positively and a negatively charged object
+
Resultant field pattern around two positively charged objects
+
+
Resultant field pattern around two negatively charged objects
-
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The electric field pattern between two charged parallel plates (Uniform field)
+
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+
+
+
+
The field lines between the plates are parallel to each other.
The same force is exerted on a small positive charge wherever it is placed in
the field.
The electric field strength is the same at any point between two parallel
charged plates.
ELECTRIC FIELD STRENGTH
Electric field strength or intensity is the measure of the force (attraction or repulsion)
exerted on a charge placed at a point in the field.
Definition: Electric field strength (E) is the force per unit charge which a positive
charge will experience at that point, i.e. force experienced by 1C of charge in an
electric field.
F
E 
Q
Electric field strength is a vector.
Therefore, the magnitude of the force exerted on a known charge in an electric field
strength is given by
F = QE
ELECTRIC FIELD STRENGTH AROUND A CHARGED SPHERE (non-uniform)
To calculate the electric field strength a distance away from a charge use
kQ
E  2
r
Q is the charge that causes the field.
If the field at a point is due to more than one charged object, the field strength must
be worked out for each charge and the resultant field strength will be
Eresultant = E1 + E2 + ….
Remember that electric field strength is a vector and, therefore, the directions must
be taken into account when calculating the resultant.
V
Electric field between 2 parallel plates formula E = where V is the voltage across
d
the plates and d the distance between the plates (m).
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ELECTRICAL POTENTIAL ENERGY & POTENTIAL DIFFERENCE
Work done in moving a charge in an electric field
Consider the following diagram:
+
+
-
+
The point charge Q experiences a force F in the
direction of the field E, and if Q is free to move,
it will accelerate in the direction of the field.
Field exerts a force on Q, causes it to move,
therefore, work is done on Q.
_
Q
+
-
W=Fxs
and F = QE
Therefore, W = QEs
∙B
A∙
ELECTRICAL POTENTIAL DIFFERENCE
A charge placed at any point in an electric field possesses potential energy.
When it moves with the field, it accelerates and so its potential is converted to kinetic
energy.
Consider an electric field around a positive sphere.
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+
A
High Ep
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If a positive charge
Q is placed at point
A, it experiences a
force of repulsion
and moves to the
right, gaining kinetic
energy as it moves.
B
Lower Ep
At A the test charge has potential.
The same charge placed at point B, has the same behaviour.
To move the charge from B to A requires an external force, i.e. work must be
done by an outside force.
This implies that Q has more potential energy at point A than at point B.
Therefore, A has a higher electrical potential energy than B, and a difference
in potential energy exists between these two points.
The potential energy in an electric field is defined as the work it takes to
move a unit positive charge from the point at lower potential to the point at
higher potential.
V=W
Q
Units: V – volts (v), W – joule (J)
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ELECTRIC FIELD STRENGTH BETWEEN TWO CHARGED PARALLEL PLATES
 The electric field strength between 2 oppositely charged parallel plates is
uniform, i.e. a charge placed anywhere between these plates will have a
constant force acting on it.
 The potential difference between the plates is given by : V = W/Q
 Therefore, work done by the field is: W = QV
 Work is also: W = QEs
 The electric field strength E = V/s or V/d s or d is the distance between
the plates in m.
QQ
Electrical potential energy
U=k 1 2
r
W
Potential difference
V =
Q
kQ
Electrical potential
V=
r
X-ample Questions
Question 1
The values in the following table were obtained during an investigation relating to
Coulomb’s Law.
EXPERIMENT ELECTROSTATIC CHARGE
NUMBER
FORCE
Q1
(X 10-5)
1
2
3
4
5
6
7
1.1
1.2
1.3
1.4
1.5
1.6
22,5
5,265
2,5
5
10
20
40
5
5
5
5
5
10
20
CHARGE DISTANCE
Q1
BETWEEN
(X 10-5) CHARGES
(m)
5
1
5
2
5
3
10
3
20
3
20
3
20
3
r2
Identify the independent, dependant and constant variables for
experiment 1, 2 and 3.
Which experiments show the relationship between force and charge Q 1?
Explain your choice.
Redraw the table and complete the table for experiment 1, 2 and 3.
1
Draw a sketch graph to show the force against 2
r
Give the relationship in 1.4
Two charges of +5 nC and -15 nC respectively are placed 5 mm apart.
Calculate the electrostatic force between the charges
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r2
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1.7
1.8
1.9
1.10
The two objects are now brought in contact and returned to their original
positions. Calculate the charge on each after touching .
How many electrons moved from the one object to the other while in
contact?
Describe the difference in the force before they touched and after they
touched
Calculate the electric field strength of the +5 nC charge at a distance
of 10 cm
(2)
(2)
(2)
(5)
Question 2
Q
15 mm
B
15 mm
A
An electric field is caused by a charge Q (-15 C). Charge q (-2C) is placed at A,
then moved to point B. A and Q are 30 mm apart.
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Calculate the electrical potential energy at point A.
Calculate the electrical potential energy at point B.
How much work is done to move q from A to B?
Calculate the potential difference between A and B.
Calculate the electrical potential of q at A.
Calculate the electrical potential of q at B.
Use your answers in 2.5 and 2.6 to confirm the potential difference
answer in question 2.4.
If q has a charge of -4C, what effect will it have on the values of
2.8.1 the electrical potential energy at A?
2.8.2 the electrical potential energy at B?
2.8.3 the electrical potential at A?
2.8.4 the electrical potential at B?
(4)
(4)
(2)
(3)
(4)
(4)
(3)
(2)
(2)
(2)
(2)
X-ercise
Question 1
Two oppositely charged objects exert a force F on one another when they are
1 m apart. Predict the new force when the distance is
1.1
doubled
1.2
tripled
1.3
halved
1.4
1.4.1 A small positive charge A is midway between two objects B and C.
B and C are identical positive charges.
What is the direction and magnitude of the resultant force on A?
1.4.2 B is now charged negatively with the same magnitude as before.
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What is the direction and magnitude of the resultant force on A?
(2)
1.5
1.5.1 Objects A and B are charged 4 x 10-5 C and -2 x 10-5 C respectively
and are placed 5 mm apart. Calculate the electrostatic force between
the objects.
1.5.2 Two insulated objects are equally but oppositely charged. They are
30 mm apart and experience a force of 2,56 x 10-3 N.
Calculate the magnitude of the charge on each object.
1.6
1.7
(4)
(5)
A charge experiences a force of 2,8 x 10-3 N when placed in an electric
field where the field strength is 7 x 105 N.C-1. What is the magnitude of
the charge?
(4)
Calculate the electric field strength between two oppositely charged
parallel plates. The plates are 90 mm apart and have a potential
difference between them of 1800 V.
(4)
Question 2
2.1
2.2
2.3
Define electrical potential energy.
Draw a diagram of two charged objects that can be used to illustrate
negative electrical potential energy.
Explain two factors that will increase the electrical potential energy.
(2)
(3)
(4)
Question 3
Two charged objects are placed as seen below. B is allowed to move to point C.
- 40
C
2,5 m
A
C
3,5 m
+
60
C
B
Charged object
A fixed on an
insulated stand
3.1
3.2
3.3
3.4
Calculate the electrical potential energy of B at its starting position.
(4)
Calculate the electrical potential energy of B once it reaches point C.
(4)
Did the electrical potential energy of B increase or decrease as it moved
to point C?
(2)
Calculate the resultant electric field strength at C.
(10)
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