Page 1 of 17
Chapter-1
Electrostatics
Content: Coulomb’s law (scalar and vector forms), electric field, electric field due to point charge, electric
dipole and its moment, electric fields along the axial and equatorial lines, concept of dielectric and dielectric
constant, Gauss’s theorem and its application to find electric field due to an infinite wire and plane sheet of
charge, conductors and insulators, force and torque experienced by a dipole(in uniform electric field),
capacitance, parallel plate capacitor with air/dielectric medium between the plates, series and parallel
combinations of capacitors, energy stored of a capacitor, numerical problems.
_______________________________________________________________________________________
Introduction: Electrostatics, as the name implies, is the study of stationary electric charges.
A rod of plastic rubbed with fur or a rod of glass rubbed with silk will attract small pieces of paper and is said
to be electrically charged. The charge on plastic rubbed with fur is defined as negative, and the charge on glass
rubbed with silk is defined as positive.
Electric charge
Charge is that property of an object by virtue of which it applies electrostatic force of interaction on other
charged objects.
Charges are of two kinds
(i) Positive charge
(ii) Negative charge
SI unit of electric charge is coulomb (C). CGS unit of charge is stat coulomb and ab coulomb.
1 coulomb= 3× 𝟏𝟎𝟗 stat coulomb
1 ab coulomb= 10 coulombs
Electrically charged objects have several important characteristics:
• Like charges repel one another; that is, positive repels positive and negative repels negative.
• Unlike charges attract each another; that is, positive attracts negative.
Characteristics of Charge
• Charge is conserved: A neutral object has no net charge. If the plastic rod and fur are initially neutral,
when the rod becomes charged by the fur, a negative charge is transferred from the fur to the rod. The net
negative charge on the rod is equal to the net positive charge on the fur.
• The additive nature of charge means that the entire electric charge of a system is equal to the algebraic sum
of electric charges located in the system. This is the law of superimposition of electric charge.
• The quantization of electric charge means that the total charge of the body is always an integral multiple
of a basic quantum of charge (e) i.e
q = ± ne where, n = 1, 2, 3, …
e = charge on an electron = 1.6 × 10−19 C
The basic cause of quantization of electric charge is that during rubbing only an integral number of electrons
can be transferred from one body to another.
1.1 Coulomb’s law (scalar and vector forms):
1.1.1 Coulomb’s law in electrostatics (scalar form):
According to Coulomb’s law, the force of attraction or repulsion between the two-point charges is
i) directly proportional to the product of the charges and
ii) inversely proportional to the square of distance between their (charges) centres.
+q1 + q2
< < > >
, Page 2 of 17
Suppose two-point charges q1 and q 2 are separated in vacuum by distance r.
𝐹 ∝ 𝑞1 𝑞2
1
𝐹∝ 2
𝑟q q q1 q 2
∴ F ∝ 1r2 2 ➔ F=k r2
k= F r2 /q1q2
Where k is electrostatics force constant. The value of k depends upon the nature of medium separating the
charges and on the system of units.
When the charges are situated in free space (air/vacuum)
In CGS system, k = 1
1
In SI system, k = 4πε = 9 × 109 Nm2 C−2
o
1
εo = =8.854×10-12 N-1m-2 C2
4πk
1 q1 q2
F= (Air/Vacuum)
4πεo r2
1 q1 q2
F = 4πε (Medium)
r2
k = ε /εo
Where εo is the absolute electrical permittivity of the free space and it is equal to 8.854×10-12 C2N-1m-2. It is
the measure of the property of medium surrounding electric charges which determine the force between the
charges. More is the permittivity of medium, less is the Coulomb’s force.
1 q1 q2
∴ F = 4πε (scalar form of Coulomb’s law)
o r2
A (vector) = A (magnitude) x unit vector
⃗F = 1 q1 q2
2 r̂ = 4πε
1 q1 q2
r
4πε o r o r 3
⃗F = 1 q1 q2
r̂ = 4πε
1 q1 q2
r
4πε r 2 r 3
Unit vector= Is a vector whose magnitude is unit (one) and direction is same as that of the vector
⃗ = AA
A ̂
r /r= r̂
, Page 3 of 17
1.1.2 Coulomb’s law in vector form:
Let r1 = ⃗⃗⃗⃗⃗
OA= Position vector of charge q1 .
And r2 = ⃗⃗⃗⃗⃗
OB= Position vector of charge q 2 .
r2 = r1 + r12 => r12 = r2 - r1
∴ The vector leading from q1 to q 2 is ⃗⃗⃗⃗⃗
AB = r12 = r2 − r1
-r21 + r1 = r2
-r21 + r1 = r2
-r21 = r2 – r1
r21 = -( r2 – r1)
r21 = r1 – r2
Similarly, vector leading from q 2 to q1 is ⃗⃗⃗⃗⃗
BA = r21 = r1 − r2
r⃗ r⃗
So, unit vectors along AB is r̂12 = r12 and along BA is r̂21 = r21
12 21
If ⃗F12 =Force on q 2 due to q1
⃗F21 =Force on q1 due to q 2
1 q1 q2
∴ ⃗F12 = 4πε along AB
o AB2
1 q1 q 2
⃗F12 = r̂
4πεo r12 2 12
1 q1 q 2
⃗F12 = r
4πεo r12 3 12
⃗F21 =Force on q1 due to q 2
1 q1 q2
⃗ 21 =
∴F along BA
4πε o BA2
1 q1 q 2
⃗F21 = r
4πεo r21 3 21
1 q1 q 2
𝐹21 = (𝑟 − 𝑟1 )
4πεo |𝑟2 − 𝑟1 |3 2
Similarly,
1 q1 q 2
𝐹12 = (𝑟 − 𝑟2 )
4πεo |𝑟1 − 𝑟2 |3 1
F12 = - F21
F21 = - F12
1.2 Electric field
Chapter-1
Electrostatics
Content: Coulomb’s law (scalar and vector forms), electric field, electric field due to point charge, electric
dipole and its moment, electric fields along the axial and equatorial lines, concept of dielectric and dielectric
constant, Gauss’s theorem and its application to find electric field due to an infinite wire and plane sheet of
charge, conductors and insulators, force and torque experienced by a dipole(in uniform electric field),
capacitance, parallel plate capacitor with air/dielectric medium between the plates, series and parallel
combinations of capacitors, energy stored of a capacitor, numerical problems.
_______________________________________________________________________________________
Introduction: Electrostatics, as the name implies, is the study of stationary electric charges.
A rod of plastic rubbed with fur or a rod of glass rubbed with silk will attract small pieces of paper and is said
to be electrically charged. The charge on plastic rubbed with fur is defined as negative, and the charge on glass
rubbed with silk is defined as positive.
Electric charge
Charge is that property of an object by virtue of which it applies electrostatic force of interaction on other
charged objects.
Charges are of two kinds
(i) Positive charge
(ii) Negative charge
SI unit of electric charge is coulomb (C). CGS unit of charge is stat coulomb and ab coulomb.
1 coulomb= 3× 𝟏𝟎𝟗 stat coulomb
1 ab coulomb= 10 coulombs
Electrically charged objects have several important characteristics:
• Like charges repel one another; that is, positive repels positive and negative repels negative.
• Unlike charges attract each another; that is, positive attracts negative.
Characteristics of Charge
• Charge is conserved: A neutral object has no net charge. If the plastic rod and fur are initially neutral,
when the rod becomes charged by the fur, a negative charge is transferred from the fur to the rod. The net
negative charge on the rod is equal to the net positive charge on the fur.
• The additive nature of charge means that the entire electric charge of a system is equal to the algebraic sum
of electric charges located in the system. This is the law of superimposition of electric charge.
• The quantization of electric charge means that the total charge of the body is always an integral multiple
of a basic quantum of charge (e) i.e
q = ± ne where, n = 1, 2, 3, …
e = charge on an electron = 1.6 × 10−19 C
The basic cause of quantization of electric charge is that during rubbing only an integral number of electrons
can be transferred from one body to another.
1.1 Coulomb’s law (scalar and vector forms):
1.1.1 Coulomb’s law in electrostatics (scalar form):
According to Coulomb’s law, the force of attraction or repulsion between the two-point charges is
i) directly proportional to the product of the charges and
ii) inversely proportional to the square of distance between their (charges) centres.
+q1 + q2
< < > >
, Page 2 of 17
Suppose two-point charges q1 and q 2 are separated in vacuum by distance r.
𝐹 ∝ 𝑞1 𝑞2
1
𝐹∝ 2
𝑟q q q1 q 2
∴ F ∝ 1r2 2 ➔ F=k r2
k= F r2 /q1q2
Where k is electrostatics force constant. The value of k depends upon the nature of medium separating the
charges and on the system of units.
When the charges are situated in free space (air/vacuum)
In CGS system, k = 1
1
In SI system, k = 4πε = 9 × 109 Nm2 C−2
o
1
εo = =8.854×10-12 N-1m-2 C2
4πk
1 q1 q2
F= (Air/Vacuum)
4πεo r2
1 q1 q2
F = 4πε (Medium)
r2
k = ε /εo
Where εo is the absolute electrical permittivity of the free space and it is equal to 8.854×10-12 C2N-1m-2. It is
the measure of the property of medium surrounding electric charges which determine the force between the
charges. More is the permittivity of medium, less is the Coulomb’s force.
1 q1 q2
∴ F = 4πε (scalar form of Coulomb’s law)
o r2
A (vector) = A (magnitude) x unit vector
⃗F = 1 q1 q2
2 r̂ = 4πε
1 q1 q2
r
4πε o r o r 3
⃗F = 1 q1 q2
r̂ = 4πε
1 q1 q2
r
4πε r 2 r 3
Unit vector= Is a vector whose magnitude is unit (one) and direction is same as that of the vector
⃗ = AA
A ̂
r /r= r̂
, Page 3 of 17
1.1.2 Coulomb’s law in vector form:
Let r1 = ⃗⃗⃗⃗⃗
OA= Position vector of charge q1 .
And r2 = ⃗⃗⃗⃗⃗
OB= Position vector of charge q 2 .
r2 = r1 + r12 => r12 = r2 - r1
∴ The vector leading from q1 to q 2 is ⃗⃗⃗⃗⃗
AB = r12 = r2 − r1
-r21 + r1 = r2
-r21 + r1 = r2
-r21 = r2 – r1
r21 = -( r2 – r1)
r21 = r1 – r2
Similarly, vector leading from q 2 to q1 is ⃗⃗⃗⃗⃗
BA = r21 = r1 − r2
r⃗ r⃗
So, unit vectors along AB is r̂12 = r12 and along BA is r̂21 = r21
12 21
If ⃗F12 =Force on q 2 due to q1
⃗F21 =Force on q1 due to q 2
1 q1 q2
∴ ⃗F12 = 4πε along AB
o AB2
1 q1 q 2
⃗F12 = r̂
4πεo r12 2 12
1 q1 q 2
⃗F12 = r
4πεo r12 3 12
⃗F21 =Force on q1 due to q 2
1 q1 q2
⃗ 21 =
∴F along BA
4πε o BA2
1 q1 q 2
⃗F21 = r
4πεo r21 3 21
1 q1 q 2
𝐹21 = (𝑟 − 𝑟1 )
4πεo |𝑟2 − 𝑟1 |3 2
Similarly,
1 q1 q 2
𝐹12 = (𝑟 − 𝑟2 )
4πεo |𝑟1 − 𝑟2 |3 1
F12 = - F21
F21 = - F12
1.2 Electric field
