Electrostatics
Electrostatics
The branch of physics that deals with the study of static charges is called
electrostatics.
Q.1
What is charge? Discuss the nature, existence and transferring of
electric charge.
(Ans) Electric charge
It is the property of a substance due to which it can attract or repel another
substance.
Nature, existence and transferring of charge
Charge is basically electric in nature. It may be positive or negative. Same
charges repel while opposite charges attract each other.Transfer of
charges can be explained by the following experiments.
Take two small pith balls that are suspended by means of a thread. In the
beginning, the two balls remain at their mean position, because they are
neutral.
If the two balls are touched with positive charge glass rod and becomes
free. These balls will repel each other and moves away from each other.
+
+
Now if one ball is touched with positive charge rod and the other with
negative charged rod and becomes free. These balls will attract each
other and moves closer to each other.
-
+
Conclusion
It is concluded from the above experiments that charge can be transferred
from one object to another. It is also concluded that similer charges repel
while opposite charges attract each other.
Q.2 How an object can be charged by rubbing?
(Ans) Charging by rubbing
A body can be charged by rubbing it with another body. It is because
some electrons from the surface of one body transferred to the surface of
other body during rubbing. For example
When a comb is rubbed with hair, the hair loses an electron and becomes
positively charge while the comb gain electron and becomes negatively
charge.
Q.3 What is meant by electrostatic induction?
(Ans) Electrostatic induction
The rearrangement of charges inside a neutral body when a charged body
is brought closer to it is called electrostatic induction.” This new
arrangement of charges is temporary and will regain original after the
removal of charged body. Electrostatic induction can take place in both
conductors and insulators.
 Charging of insulators by induction
When a comb is rubbed with hair, the comb gains negative charge due to
the accumulation of charges from the hair over it. When this comb is
brought closer to a neutral body such as a piece of paper, then the
electrons push locally away, whereas the positively charged protons
remain at their original position. Thus the attractive forces become
stronger as compared to the repulsive forces and the piece of paper is
attracted towards the comb. This separation of positive and negative
charges inside the insulator is known as polarization of insulators
 Charging a conductor by induction
Take a metallic sphere that is fixed on an insulated stand. When a positive
charge glass rod is brought closer to the sphere. The rearrangement of
charges takes place inside the metallic sphere. The negative charges
come closer to the positive charged glass rod. In this way, a conductor is
charged by induction.
Q.4 Write a note on Electroscope.
(Ans) Electroscope
A sensitive device used for the detection and testing of charge is called
Electroscope.
Construction
It consists of a metallic rod, whose one end is connected to a disc while at
the other end two gold leaves are attached. The rod is fitted in a glass
case as shown in figure.
Detection of charge
In order to detect the presence of charge on a body, bring it near the disc
of an uncharged electroscope. If the body is charged, the leaves of the
electroscope diverge to a definite extent.
If the body is uncharged then the leaves remain at their normal position.
Testing the nature of charge
In order to test a charge, we need to charge the Electroscope first by
placing a negative charge on the disc. In this way, the leaves become
negatively charged. Now bring the testing charge body near the disc. If the
leaves diverged, the charge will be negative. If the leaves collapse, the
charge will be positive.
Q.5 State and explain Coulombs law?
(Ans) Statement
This law states that “the force of attraction or repulsion between the two
charges is directly proportional to the product of the magnitude of charges
and inversely proportional to the square of the distance between the
charges.”
Explanation
Consider two spherical charges “q1” and “q2” are placed at a distance“r”
from each other as shown in figure.
r
q1
q2
Mathematical expression
F  q1q2    (1)
F 
1
     (2)
r2
Combining equation (1) and (2) we get
F
q1q2
r2
F  (Constt)
F k
q1q2
r2
q1q2
r2
Where “k” is constant of proportionality and it is known Coulombs constant,
its value is 9  10 9 Nm2/C2.
k
1
4 
F
1 q1 q 2
4  r 2
Q.6 What is meant by electric field and electric field intensity?
(Ans) Electric field
The region around a charge body in which it can interact another charge is
known as electric field. It is a vector quantity. It is represented by electric
lines of force.
Electric field intensity
The strength of the field at any point is known as electric field intensity.
It can also be defined as “the electric force exerted per unit positive test
charge is known as electric field intensity. It is denoted by “E”. It is a vector
quantity. Mathematically

 F
E
q

qq
F  k 2
r

qq
q
Ek

k
q r 2
r2
This equation shows the electric field intensity of a point charge “q”.
The SI unit of electric field intensity is Newton/coulomb (N/C).
Q.7 What are electric lines of force? Describe its characteristics.
(Ans) Eectric lines of force
An electric line of force in general shows the path through which an
electric charge would move. The direction of the lines shows the direction
of the field. The number of electric lines per unit area represents the
intensity of the field.
General characteristics of the electric lines of force are as under:
 A positive charge always emits lines of force.
 A negative charge always absorbe lines of force.
 When two opposite charges are placed nearer, then the lines of force start
from the positive charge and ends at negative charge. As a result, they
attract each other.
 When two identical charges are placed nearer, the lines of force behave
as shown in figure.
 Consider two infinite oppositely charge plates are placed parallel to each
other. The electric lines of force emit from positive charge and absorbe by
the negative charge. The lines of force are straight and parallel at the
centre of the plates. Whereas at the ends of the plates, the lines of force
are a little bulging out. This shows that the field is uniform at the centre
and non-uniform at the ends of the plates.
Q.8 Define and explain electric potential and its unit?
(Ans) Electric potential
The work done on a unit positive charge to move it from one place to
another against the electric field is called electric potential. It is denoted by
“V”. Mathematically
V 
W
q
Potential difference
The work done on a unit positive charge to move it from point “A” to point
“B” against the electric field is called potential difference. OR
The energy supplied by a unit positive charge as it moves from a point of
higher potential to a point of lower potential is called potential difference.
It is denoted by “ V ”. Mathematically
W A B
q
V  V A  V B
V 
W A B
q
 q (V A  VB )
V A  VB 
W A B
Q.9 Write the practical applications of electrostatics.
(Ans) The practical applications of electrostatics are as under:
(1)
Electropainting
Electrostatics is used in applying paint on the surface of different articles.
The body of the car is earthed. The particles of the paint emerge out of the
nozzle of the spray machine, they aquire a positive charge. As they
reached to the body of the car due to electrostatic induction negative
induced on the body of the car. As a result, an electrostatic force
established and firm coating of the paint is formed on the surface of the
car. This method is efficient, effective and cheap.
(2)
Dust extraction
Electrostatics is used for the separation of smoke and dust particles from
a coal-burning power station by means of an electroastatic precipitator.
Q.10 What is a capacitor? Describe the capacitance of a capacitor.
(Ans) Capacitor
A device used to store an electric charge is called capacitor.
Construction
A capacitor consists of two parallel metallic plates having a small distance
between them. The medium inside the plates is air or some other
insulating material known as dielectric.
Charging a capacitor
Consider a charge “+Q” is transferred to plate A, then by electrostatic
induction a “-Q” charge is induced on plate B.
A force of attraction is established between the plates due to which the
charges are bound with the plates and remain stored for long period.
Capacitance of a capacitor
The capacity of a capacitor to store charge is called capacitance of the
capacitor.
Experiments show that the charge store in a capacitor is directly
proportion to the potential difference across the plates of the capacitor.
Mathematically
Q V
Q  CONSTANT (V )
Q  CV
Where “C” is costant and is known as capacitance of the capacitor. The SI
unit of capacitance of a capacitor is farad (F).
Farad
It can be defined as “the capacitance of a capacitor is one farad if one
coulomb charge is stored by the capacitor providing a potential difference
of one volt to their plates.”
Q.11 How capacitors can be connected in a circuit?
(Ans) There are two basic ways of connecting capacitors in a circuit.
1. Series combination
A type of combination of two or more than two capacitors in which the
capacitors are connected plate to plate is called series combination of the
capacitors.
Explanation
Consider three capacitors of capacitance c1, c2 and c3 are connected in
series. A battery of voltage “V” is connected to the circuit. The battery
provide a positive charge “Q” to the left plate of capacitor C1 due to
electrostatic induction a negative charge is induced on the right plate and
charges distribute on the other plates similarly.
The flow of charges to each capacitor is constant in series combination.
Q1  Q2  Q3  Q
Voltage across each capacitor decreases. The sum of all the voltage
across the capacitors is equal to the total voltage.
V  V1  V2  V3
We know that
Q
V 
Q  CV 
C
V  V1  V2  V3
Q
Q
Q
Q
 1  2  3
Ceq
C1 C2
C3
Q
Q
Q
Q



Ceq
C1 C2 C3
Q
1
1
1
 Q(


)
Ceq
C1 C2 C3
1
1
1
1



Ceq
C1 C2 C3
Now for “n” number of capacitor the formula can be written as;
1
1
1
1
1




Ceq
C1
C2
C3
Cn
Similarly for two capacitor C1 and C2 the formula becomes;
1
1
1


Ceq
C1 C2
1
C  C1
 2
Ceq
C1C2
Ceq 
C1C2
C1  C2
2. Parallel combination of capacitor
A type of combination of two or more than two capacitors in which the
plates of the capacitors are connected parallel to each other as shown in
figure is called parallel combination of capacitors.
Explanation
Consider three capacitors of capacitance c1, c2 and c3 are connected in
series. A battery of voltage “V” is connected to the circuit. The battery
provide a positive charge “Q” to the left plate of capacitor C1 due to
electrostatic induction a negative charge is induced on the right plate and
charges distribute on the other plates similarly.
The voltage across each capacitor remains constant in parallel
combination of capacitors.
V1  V2  V3  V
The flow of charge to each capacitor is distributed in parallel combination
of capacitors. The total charge is equal to the sum of charge across each
capacitor.
Q  Q1  Q2  Q3 ----------- (A)
We know that
Q  CV
Qeq  CeqVeq , Q1  C1V1 , Q2  C2V2 , Q3  C 3V3
Put these values in equation (A)
CeqVeq  C1V1  C2V2  C3V3
As
V1  V2  V3  V
C eqV  C1V  C 2V  C 3V
C eq  C1  C 2  C 3
For "n" numbers of capacitors, we have
Ceq  C1  C2  C3        Cn
Q.12 Write different types of capacitors.
(Ans) There are two types of capacitors.
1. Fixed capacitors
2. variable capacitors
1. Fixed capacitors
Those capacitors whose parts are fixed by design and its plates are
immovable is called fixed capacitors. The capacitance of these capacitors
does not change (constant). Examples of these capacitors are paper
capacitors and mica capacitors.
2. Variable capacitors
A type of capacitors whose area of the plates can be changed is called
variable capacitors. The capacitance of these capacitors can be changed
by increasing or decreasing the area between the plates. For example
The capacitors used in tuning of a radio frequency.
(Fixed capacitors)
(Variable capacitors)
SHORT QUESTIONS
1.
A.
2.
A.
3.
A.
A balloon is negatively charged by rubbing and then clings to a wall.
Does this mean that the wall is positively charged? Why does the
balloon eventually fall?
The wall is neutral in the beginning, when we brought a negatively
charged balloon closer to the wall. Due to electrostatic induction, the
positive charges present in the wall moves forward to attract the balloon.
As a result, the balloon sticks with the wall for a while.
The negative charges of balloon neutralized the positive charges induced
on the wall due to the transferred of charges. Now as a result the balloon
eventually falls.
Why is it not good to seek shelter under a tree during a lightning
storm?
it is not a good idea to seek shelter under a tree during a lightning storm.
Because when the charge clouds pass over a tree, then an opposite
charge is induced on the tree due to electrostatic induction. The force of
attraction is established between the tree and clouds due to which there is
a greater possibility for the lightning discharge to take place.
A charge comb often attracts small bits of dry paper that then fly
away when they touch the comb. Explain?
See Q.3 (charging an insulator by induction).
4.
A.
Define the term volt?
Volt is the SI unit of potential difference. It can be defined as “if 1 joule
work is done on a charge body of 1 coulomb to move it from one point to
another against the electric field.” Mathematically
1 joule
1Volt 
1coulomb
5.
A.
What is meant by electrostatic induction?
See Q.3
6.
A.
What is meant by charging an object electrically?
To make an electrical contact between the object and the earth by a
conducting wire is known as earthing an object electrically. By doing so
the additional charge will flow towards the earth surface.
7.
Two isolated copper sphere, A and B, are initially uncharged. They
are placed near each other as shown in figure. What is the charge
distribution on A when B is given a negative charge?
A.
The rearrangement of charges occurs in A due to electrostatic induction.
Positive charges present in A move towards the negative charges on B,
while negative charges present in A moves away to the other side as
shown in the figure.
8.
A.
Why electric charge is produced on bodies by friction?
Electric charge is produced on bodies by friction. Because when two
bodies rubbed with each other, transferred of charges occur. As a result,
charges are produced on the objects. For example
When a glass rod is rubbed with silk. The glass rod loses electrons and
the silk gain these electrons. The glass becomes positively charged, while
the silk becomes negatively charged.
9.
Two capacitors with capacitance 1µF and 0.01µF are charged to the
same potential. Which will give more intense shock if touched?
The charge stored in the capacitors depends on the capacitance of the
capacitor if voltage across the capacitor is constant. Greater the
capacitance greater will be the charge store. Therefore, the capacitor
having capacitance 1µF give more intense shock as compared to the
capacitor of capacitance 0.01µF.
A.
10.
A.
As shown in the figure a chain is hanging from the rear side of petrol
supply tanker. What is its purpose?
When the petrol supply tanker moves on a road, charge may be induced
on its body due to friction. To avoid these charges a chain is made to hang
from the rear side of petrol supply tanker. This chain works like earth wire
and supply these charges to the earth.
11.
A.
The tyres of an aircraft are made from special rubber that conducts
electricity. Explain why?
The tyres of an aircraft are made from special rubber that conducts
electricity. It is because charges are induced on the tyres due to friction
between the tyres and the ground. To transferred these charges to the
ground the tyres of an aircraft are made from a special conducting rubber
to work as earth wire.
NUMERICAL PROBLEMS
1.
Two charges 5µC and 15µC are placed at a distance of 100cm. Find
the Coulombs force between them.
Given data
q1  5C  5  10 6 C
q 2  15C  15  10 6 C
r  100cm  1m
K  9  109 Nm 2 / C 2
F ?
We know that
qq
F  K 1 22
r
(5  10 6 )(15  10 6 )
F  9  109
(1) 2
F  675  109 6 6
F  675  10 3
F  0  675N
2.
Two identical charges are 25cm apart. They repel each other with a
force of 2x10-6N. Find each charge?
Given data
q  q  q ( say)  ?
r  25cm  0.25m
F  2  106 N
K  9  109 Nm 2 / C 2
We know that
q1 q 2
r2
qq
F K 2
r
F K
Fr 2
K
 q2
( 2  10 6 )(0  25) 2
9  109
( 2  10 6 )(0  0625)
q2 
9  109
0  125  10 6
2
q 
 10 9
9
2
q  0  01389 10 69
q2 
q 2  13  89  10 6 9 3  13  89  10 18
q  13  89  10 18  3  72  10 9 C
3.
How far apart must the charge of +5.0x10-6 and -4.0x10-6 to be in
order that the charges attract each other with a force 0f 2.2N?
Given data
q1  5  0  10 6 C
q 2  4  0  10 6 C
K  9  109 Nm 2 / C 2
F  2  2N
r ?
We know that
qq
F  K 1 22
r
qq
r2  K 1 2
F
(5  10 6 )(4  10 6 )
r 2  9  109
22
Negative sign shows that force is attractive.
(5  10 6 )(4  10 6 )
r 2  9  109
22
180
 10966
22
r 2  81 81 10 3
r2 
r 2  8  181 10  2
r  2  86  10 1  0  286m
4.
When a 10µC charge is placed at a point in an electric field, it experience
a force of 10-4N. Find the value of electric field intensity at this point.
Given data
q  10C  10  106 C
F  104 N
E ?
We know that
E
E
E
E
E
E
5.
F
q
10  4

10  10  6
10  4

 10 6
10
10  4  6

10
10 2

10
 10 N / C
Three capacitors of capacitance 100µF, 200µF and 300µF are
connected in parallel. Find the equivalent capacitance of the
combination. If a battery of 12V is connected across the combination,
find the charge on each capacitor.
Given data
C1  100F  100  106 F
C 2  200F  200  106 F
C3  300F  300  106 F
V  12V
C eq  ?
q1  ?
q2  ?
q3  ?
We know that
C eq  C1  C 2  C 3
C eq  100  200  300
C eq  600F
We also know that
Q  CV
Q1  C1V  100  106  12  1200C  1  2mC
Q2  C 2V  200  106  12  2400C  2  4mC
Q3  C3V  300  106  12  3600C  3  6mC
6.
The potential difference between two points is 110V. If an unknown
charge is moved between these points, the amount of work done
is550J. Find the amount of charge?
Given data
V  110V
W  550J
Q?
We know that
W
Q
W
550
Q

 5C
V
110
V 