Electrostatics | Physics Optional Notes for UPSC PDF Download

 Page 1


Electrostatics 
ELECTRIC CHARGE 
Charge is a property of matter that causes it to create and feel electrical and magnetic 
effects. When a body has an excess or shortage of electrons, it is said to have a charge. 
SI unit of charge: ampere × second i.e. Coulomb Dimension: [A T] 
Practical units of charge are ampere × hour ( =3600C ) and faraday ( =96500C ) 
? Millikan calculated the quanta of charge by the 'Highest common factor' (H.C.F.) 
method and it is equal to the charge of an electron. 
? 1C=3×10
9
 State coulomb, 1 absolute - coulomb =10C,1 Faraday =96500C . 
? Charge is a scalar quantity: It represents excess or deficiency of electrons. 
? Charge is transferable: If a charged body is put in contact with another body, then 
the charge can be transferred to another body. 
? Charge is always associated with mass 
Charge cannot exist without mass though mass can exist without charge. 
? So the presence of charge itself is a convincing proof of the existence of mass. 
? In charging, the mass of a body changes. 
? When the body is given a positive charge, its mass decreases. 
? When a body is given a negative charge, its mass increases. 
Additivity of Charges: 
Charges add like real numbers. 
Example. 5C+6C=11C 
5C+(-6C)=-1C 
-5C+6C=1C 
-5C+5C=0C 
? Charge is quantized 
The quantization of electric charge is the property by virtue of which all free charges are 
integral multiple of a basic unit of charge represented by e. Thus charge q of a body is 
always given by 
Page 2


Electrostatics 
ELECTRIC CHARGE 
Charge is a property of matter that causes it to create and feel electrical and magnetic 
effects. When a body has an excess or shortage of electrons, it is said to have a charge. 
SI unit of charge: ampere × second i.e. Coulomb Dimension: [A T] 
Practical units of charge are ampere × hour ( =3600C ) and faraday ( =96500C ) 
? Millikan calculated the quanta of charge by the 'Highest common factor' (H.C.F.) 
method and it is equal to the charge of an electron. 
? 1C=3×10
9
 State coulomb, 1 absolute - coulomb =10C,1 Faraday =96500C . 
? Charge is a scalar quantity: It represents excess or deficiency of electrons. 
? Charge is transferable: If a charged body is put in contact with another body, then 
the charge can be transferred to another body. 
? Charge is always associated with mass 
Charge cannot exist without mass though mass can exist without charge. 
? So the presence of charge itself is a convincing proof of the existence of mass. 
? In charging, the mass of a body changes. 
? When the body is given a positive charge, its mass decreases. 
? When a body is given a negative charge, its mass increases. 
Additivity of Charges: 
Charges add like real numbers. 
Example. 5C+6C=11C 
5C+(-6C)=-1C 
-5C+6C=1C 
-5C+5C=0C 
? Charge is quantized 
The quantization of electric charge is the property by virtue of which all free charges are 
integral multiple of a basic unit of charge represented by e. Thus charge q of a body is 
always given by 
q= ne 
n= positive integer or negative integer 
The quantum of charge is the charge that an electron or proton carries. 
{Note: Charge on a proton =(-) charge on an electron =1.6×10
-19
C} 
? Charge is conserved 
In a closed system, the total amount of charge remains constant over time, even though 
individual charges can change. This means that a charge cannot be made or destroyed; it 
stays the same. This principle, called conservation of charge, applies to all types of 
reactions, whether they are chemical (atomic) or nuclear. There are no known exceptions 
to this rule. Charge is invariant 
Charge is independent of the frame of reference. i.e. charge on a body does not change 
whatever its speed. 
? Attraction-Repulsion 
Similar charges repel each other while dissimilar ones attract 
METHODS OF CHARGING 
? Friction: If we rub one body with another body, electrons are transferred from 
one body to the other. 
-   Electrostatic induction 
 
When a charged object is brought close to a neutral metal object, it causes the metal 
object to attract opposite charges and repel similar charges within itself. This leads to 
one side of the metal object becoming negatively charged while the other becomes 
positively charged. This phenomenon is known as "electrostatic induction.". 
? Charging a body by induction (in four successive steps) 
 
Some important facts associated with induction- 
(i) Inducing body neither gains nor loses charge 
Page 3


Electrostatics 
ELECTRIC CHARGE 
Charge is a property of matter that causes it to create and feel electrical and magnetic 
effects. When a body has an excess or shortage of electrons, it is said to have a charge. 
SI unit of charge: ampere × second i.e. Coulomb Dimension: [A T] 
Practical units of charge are ampere × hour ( =3600C ) and faraday ( =96500C ) 
? Millikan calculated the quanta of charge by the 'Highest common factor' (H.C.F.) 
method and it is equal to the charge of an electron. 
? 1C=3×10
9
 State coulomb, 1 absolute - coulomb =10C,1 Faraday =96500C . 
? Charge is a scalar quantity: It represents excess or deficiency of electrons. 
? Charge is transferable: If a charged body is put in contact with another body, then 
the charge can be transferred to another body. 
? Charge is always associated with mass 
Charge cannot exist without mass though mass can exist without charge. 
? So the presence of charge itself is a convincing proof of the existence of mass. 
? In charging, the mass of a body changes. 
? When the body is given a positive charge, its mass decreases. 
? When a body is given a negative charge, its mass increases. 
Additivity of Charges: 
Charges add like real numbers. 
Example. 5C+6C=11C 
5C+(-6C)=-1C 
-5C+6C=1C 
-5C+5C=0C 
? Charge is quantized 
The quantization of electric charge is the property by virtue of which all free charges are 
integral multiple of a basic unit of charge represented by e. Thus charge q of a body is 
always given by 
q= ne 
n= positive integer or negative integer 
The quantum of charge is the charge that an electron or proton carries. 
{Note: Charge on a proton =(-) charge on an electron =1.6×10
-19
C} 
? Charge is conserved 
In a closed system, the total amount of charge remains constant over time, even though 
individual charges can change. This means that a charge cannot be made or destroyed; it 
stays the same. This principle, called conservation of charge, applies to all types of 
reactions, whether they are chemical (atomic) or nuclear. There are no known exceptions 
to this rule. Charge is invariant 
Charge is independent of the frame of reference. i.e. charge on a body does not change 
whatever its speed. 
? Attraction-Repulsion 
Similar charges repel each other while dissimilar ones attract 
METHODS OF CHARGING 
? Friction: If we rub one body with another body, electrons are transferred from 
one body to the other. 
-   Electrostatic induction 
 
When a charged object is brought close to a neutral metal object, it causes the metal 
object to attract opposite charges and repel similar charges within itself. This leads to 
one side of the metal object becoming negatively charged while the other becomes 
positively charged. This phenomenon is known as "electrostatic induction.". 
? Charging a body by induction (in four successive steps) 
 
Some important facts associated with induction- 
(i) Inducing body neither gains nor loses charge 
(ii) The nature of induced charge is always opposite to that of inducing charge 
(iii) Induction takes place only in bodies (either conducting or non conducting) and not 
in particles. 
- Conduction 
? The method of transferring charge by touching two objects is called conduction. 
When a charged object comes into contact with an uncharged object, the 
uncharged object becomes charged because electrons are transferred from one 
object to the other. 
? The charged body loses some of its charge (which is equal to the charge gained by 
the uncharged body) 
? The charge gained by the uncharged body is always lesser than initial charge 
present on the charged body. 
COULOMB'S LAW 
According to this law electrostatic force acting between two point charges ( q
1
 and q
2
 ) 
kept at distance ?? is given by. 
?? =
1
4?? ?? 0
×
?? ?? 1
?? 2
?? 2
 
Where ?? 0
 is called permittivity of free sphace (vacuum) 
?? 0
=8.85×10
-12
]
[ Unit =
C
2
 N-m
2
] We take 
1
4?? ?? 0
=k
F=
kq
1
q
2
r
2
  where k=9×10
9
1?? C=10
-6
C
1?? C=10
-9
C
 
Example. Find the dimension of ?? 0
 
Solution: [?? 0
]=
C
2
 N-m
2
=
(IT)
2
(MLT
-2
)
×
L
2
=I
2
 T
4
M
-1
 L
-3
 
? By "point charges" we mean that charged bodies are very small as compared to 
the distance between them. 
? The force F appearing in the equation is the magnitude of electrostatic force 
applied by one charged body on another and vice-versa. 
Coulomb's law in vector form: 
Page 4


Electrostatics 
ELECTRIC CHARGE 
Charge is a property of matter that causes it to create and feel electrical and magnetic 
effects. When a body has an excess or shortage of electrons, it is said to have a charge. 
SI unit of charge: ampere × second i.e. Coulomb Dimension: [A T] 
Practical units of charge are ampere × hour ( =3600C ) and faraday ( =96500C ) 
? Millikan calculated the quanta of charge by the 'Highest common factor' (H.C.F.) 
method and it is equal to the charge of an electron. 
? 1C=3×10
9
 State coulomb, 1 absolute - coulomb =10C,1 Faraday =96500C . 
? Charge is a scalar quantity: It represents excess or deficiency of electrons. 
? Charge is transferable: If a charged body is put in contact with another body, then 
the charge can be transferred to another body. 
? Charge is always associated with mass 
Charge cannot exist without mass though mass can exist without charge. 
? So the presence of charge itself is a convincing proof of the existence of mass. 
? In charging, the mass of a body changes. 
? When the body is given a positive charge, its mass decreases. 
? When a body is given a negative charge, its mass increases. 
Additivity of Charges: 
Charges add like real numbers. 
Example. 5C+6C=11C 
5C+(-6C)=-1C 
-5C+6C=1C 
-5C+5C=0C 
? Charge is quantized 
The quantization of electric charge is the property by virtue of which all free charges are 
integral multiple of a basic unit of charge represented by e. Thus charge q of a body is 
always given by 
q= ne 
n= positive integer or negative integer 
The quantum of charge is the charge that an electron or proton carries. 
{Note: Charge on a proton =(-) charge on an electron =1.6×10
-19
C} 
? Charge is conserved 
In a closed system, the total amount of charge remains constant over time, even though 
individual charges can change. This means that a charge cannot be made or destroyed; it 
stays the same. This principle, called conservation of charge, applies to all types of 
reactions, whether they are chemical (atomic) or nuclear. There are no known exceptions 
to this rule. Charge is invariant 
Charge is independent of the frame of reference. i.e. charge on a body does not change 
whatever its speed. 
? Attraction-Repulsion 
Similar charges repel each other while dissimilar ones attract 
METHODS OF CHARGING 
? Friction: If we rub one body with another body, electrons are transferred from 
one body to the other. 
-   Electrostatic induction 
 
When a charged object is brought close to a neutral metal object, it causes the metal 
object to attract opposite charges and repel similar charges within itself. This leads to 
one side of the metal object becoming negatively charged while the other becomes 
positively charged. This phenomenon is known as "electrostatic induction.". 
? Charging a body by induction (in four successive steps) 
 
Some important facts associated with induction- 
(i) Inducing body neither gains nor loses charge 
(ii) The nature of induced charge is always opposite to that of inducing charge 
(iii) Induction takes place only in bodies (either conducting or non conducting) and not 
in particles. 
- Conduction 
? The method of transferring charge by touching two objects is called conduction. 
When a charged object comes into contact with an uncharged object, the 
uncharged object becomes charged because electrons are transferred from one 
object to the other. 
? The charged body loses some of its charge (which is equal to the charge gained by 
the uncharged body) 
? The charge gained by the uncharged body is always lesser than initial charge 
present on the charged body. 
COULOMB'S LAW 
According to this law electrostatic force acting between two point charges ( q
1
 and q
2
 ) 
kept at distance ?? is given by. 
?? =
1
4?? ?? 0
×
?? ?? 1
?? 2
?? 2
 
Where ?? 0
 is called permittivity of free sphace (vacuum) 
?? 0
=8.85×10
-12
]
[ Unit =
C
2
 N-m
2
] We take 
1
4?? ?? 0
=k
F=
kq
1
q
2
r
2
  where k=9×10
9
1?? C=10
-6
C
1?? C=10
-9
C
 
Example. Find the dimension of ?? 0
 
Solution: [?? 0
]=
C
2
 N-m
2
=
(IT)
2
(MLT
-2
)
×
L
2
=I
2
 T
4
M
-1
 L
-3
 
? By "point charges" we mean that charged bodies are very small as compared to 
the distance between them. 
? The force F appearing in the equation is the magnitude of electrostatic force 
applied by one charged body on another and vice-versa. 
Coulomb's law in vector form: 
F
? 
12
= force on q
1
 due to q
2
=
kq
1
q
2
r
2
r ˆ
21
F
? 
21
=
kqq
1
q
2
r
2
r ˆ
12
 (here r ˆ
12
 is unit vector from q
1
 to q
2
 ) 
 
 
Coulomb's law in terms of position vector: 
F
? 
12
=
kqq
1
q
2
|r 
1
-r 
2
|
3
(r 
1
-r 
2
) 
 
Principle of superposition: 
When several charges are interacting, the total force on a given charge is vector sum of 
the forces exerted on it by all other charges individually ?? =
?? ?? 0
?? 1
?? 1
2
+
?? ?? 0
?? 2
?? 2
2
+?+
?? ?? 0
?? ?? ?? ?? 2
+
?
?? ?? 0
?? ?? ?? ?? 2
 in vector form ?? 
=kq
0
?
i=1
n
?
q
i
r
i
2
r ˆ
i
 
? The law is based on physical observations and is not logically derivable from any 
other concept. Experiments till today reveal its universal nature. 
? The force is a two-body interaction, i.e., the electrical force between two point 
charges is independent of the presence or absence of other charges and so the 
principle of superposition is valid, i.e., force on a charged particle due to a 
number of point charges is the resultant of forces due to individual point charges, 
i.e., F
? 
1
=F
? 
12
+F
? 
13
+?. 
? The net Coulomb's force on two charged particles in free space and in a medium 
filled up to infinity is 
F=
1
4?? ?? 0
q
1
q
2
r
2
 and F
'
=
1
4????
q
1
q
2
r
2
. So 
F
F
'
=
?? ?? 0
=?? ,  
? The dielectric constant (K) of a medium is numerically equal to the ratio of the 
force on two point charges in free space to that in the medium filled up to infinity. 
? The law expresses the force between two point charges at rest. In applying it to 
the case of extended bodies of finite size care should be taken in assuming the 
Page 5


Electrostatics 
ELECTRIC CHARGE 
Charge is a property of matter that causes it to create and feel electrical and magnetic 
effects. When a body has an excess or shortage of electrons, it is said to have a charge. 
SI unit of charge: ampere × second i.e. Coulomb Dimension: [A T] 
Practical units of charge are ampere × hour ( =3600C ) and faraday ( =96500C ) 
? Millikan calculated the quanta of charge by the 'Highest common factor' (H.C.F.) 
method and it is equal to the charge of an electron. 
? 1C=3×10
9
 State coulomb, 1 absolute - coulomb =10C,1 Faraday =96500C . 
? Charge is a scalar quantity: It represents excess or deficiency of electrons. 
? Charge is transferable: If a charged body is put in contact with another body, then 
the charge can be transferred to another body. 
? Charge is always associated with mass 
Charge cannot exist without mass though mass can exist without charge. 
? So the presence of charge itself is a convincing proof of the existence of mass. 
? In charging, the mass of a body changes. 
? When the body is given a positive charge, its mass decreases. 
? When a body is given a negative charge, its mass increases. 
Additivity of Charges: 
Charges add like real numbers. 
Example. 5C+6C=11C 
5C+(-6C)=-1C 
-5C+6C=1C 
-5C+5C=0C 
? Charge is quantized 
The quantization of electric charge is the property by virtue of which all free charges are 
integral multiple of a basic unit of charge represented by e. Thus charge q of a body is 
always given by 
q= ne 
n= positive integer or negative integer 
The quantum of charge is the charge that an electron or proton carries. 
{Note: Charge on a proton =(-) charge on an electron =1.6×10
-19
C} 
? Charge is conserved 
In a closed system, the total amount of charge remains constant over time, even though 
individual charges can change. This means that a charge cannot be made or destroyed; it 
stays the same. This principle, called conservation of charge, applies to all types of 
reactions, whether they are chemical (atomic) or nuclear. There are no known exceptions 
to this rule. Charge is invariant 
Charge is independent of the frame of reference. i.e. charge on a body does not change 
whatever its speed. 
? Attraction-Repulsion 
Similar charges repel each other while dissimilar ones attract 
METHODS OF CHARGING 
? Friction: If we rub one body with another body, electrons are transferred from 
one body to the other. 
-   Electrostatic induction 
 
When a charged object is brought close to a neutral metal object, it causes the metal 
object to attract opposite charges and repel similar charges within itself. This leads to 
one side of the metal object becoming negatively charged while the other becomes 
positively charged. This phenomenon is known as "electrostatic induction.". 
? Charging a body by induction (in four successive steps) 
 
Some important facts associated with induction- 
(i) Inducing body neither gains nor loses charge 
(ii) The nature of induced charge is always opposite to that of inducing charge 
(iii) Induction takes place only in bodies (either conducting or non conducting) and not 
in particles. 
- Conduction 
? The method of transferring charge by touching two objects is called conduction. 
When a charged object comes into contact with an uncharged object, the 
uncharged object becomes charged because electrons are transferred from one 
object to the other. 
? The charged body loses some of its charge (which is equal to the charge gained by 
the uncharged body) 
? The charge gained by the uncharged body is always lesser than initial charge 
present on the charged body. 
COULOMB'S LAW 
According to this law electrostatic force acting between two point charges ( q
1
 and q
2
 ) 
kept at distance ?? is given by. 
?? =
1
4?? ?? 0
×
?? ?? 1
?? 2
?? 2
 
Where ?? 0
 is called permittivity of free sphace (vacuum) 
?? 0
=8.85×10
-12
]
[ Unit =
C
2
 N-m
2
] We take 
1
4?? ?? 0
=k
F=
kq
1
q
2
r
2
  where k=9×10
9
1?? C=10
-6
C
1?? C=10
-9
C
 
Example. Find the dimension of ?? 0
 
Solution: [?? 0
]=
C
2
 N-m
2
=
(IT)
2
(MLT
-2
)
×
L
2
=I
2
 T
4
M
-1
 L
-3
 
? By "point charges" we mean that charged bodies are very small as compared to 
the distance between them. 
? The force F appearing in the equation is the magnitude of electrostatic force 
applied by one charged body on another and vice-versa. 
Coulomb's law in vector form: 
F
? 
12
= force on q
1
 due to q
2
=
kq
1
q
2
r
2
r ˆ
21
F
? 
21
=
kqq
1
q
2
r
2
r ˆ
12
 (here r ˆ
12
 is unit vector from q
1
 to q
2
 ) 
 
 
Coulomb's law in terms of position vector: 
F
? 
12
=
kqq
1
q
2
|r 
1
-r 
2
|
3
(r 
1
-r 
2
) 
 
Principle of superposition: 
When several charges are interacting, the total force on a given charge is vector sum of 
the forces exerted on it by all other charges individually ?? =
?? ?? 0
?? 1
?? 1
2
+
?? ?? 0
?? 2
?? 2
2
+?+
?? ?? 0
?? ?? ?? ?? 2
+
?
?? ?? 0
?? ?? ?? ?? 2
 in vector form ?? 
=kq
0
?
i=1
n
?
q
i
r
i
2
r ˆ
i
 
? The law is based on physical observations and is not logically derivable from any 
other concept. Experiments till today reveal its universal nature. 
? The force is a two-body interaction, i.e., the electrical force between two point 
charges is independent of the presence or absence of other charges and so the 
principle of superposition is valid, i.e., force on a charged particle due to a 
number of point charges is the resultant of forces due to individual point charges, 
i.e., F
? 
1
=F
? 
12
+F
? 
13
+?. 
? The net Coulomb's force on two charged particles in free space and in a medium 
filled up to infinity is 
F=
1
4?? ?? 0
q
1
q
2
r
2
 and F
'
=
1
4????
q
1
q
2
r
2
. So 
F
F
'
=
?? ?? 0
=?? ,  
? The dielectric constant (K) of a medium is numerically equal to the ratio of the 
force on two point charges in free space to that in the medium filled up to infinity. 
? The law expresses the force between two point charges at rest. In applying it to 
the case of extended bodies of finite size care should be taken in assuming the 
whole charge of a body to be concentrated at its 'center' as this is true only for 
spherical charged body, that too for external point. 
Although net electric force on both particles changes in the presence of dielectric but 
force due to one charge particle on another charge particle does not depend on the 
medium between them. 
Example. 
 
Find net force on Q 
Solution: Suppose 
?????? ?? 2
=?? 
F
AO
=
kQq
a
2
=F
?? ????
=
?? (2?? )?? ?? 2
=2?? F
CO
=3 F
?? ????
=?? 
 
Example. 
 
Find net force on charge at ?? 
Solution: vF
2
+F
2
+2 F
2
cos 60
°
=v3 F