ELECTROSTATICS:-
*Electrostatics deals with the study of forces, fields and potentials arising from static charges
FRICTIONAL ELECTRICITY:-
*The electricity produced by rubbing suitable bodies is called frictional electricity.
*On rubbing electrons are transferred from one body to the other. The body, which loses electrons, will become positively charged and which gains electrons becomes negatively charged.
ELECTRIC CHARGE
From simple experiments on frictional electricity, it is inferred that there are two types of charges in nature-Positive and Negative .
Like charges repel and unlike charges attract.
* When a glass rod is rubbed with silk, glass rod becomes positively charged and silk negative.
* When a plastic rod is rubbed with fur, plastic rod becomes negatively charged and fur positive.
1. Good conductors like copper cannot be charged by friction because any charge produced on it can easily flow through the rod through our body and to the ground.
2. Insulators like plastic, ebonite, glass etc. can be easily charged by friction because the charges will stay on them.
3. Electrostatic experiments cannot be performed in moist climate because moist air is slightly conducting. So the static charges will get conducted away from the charged body.
How is frictional electrification caused?
The number of protons inside the nucleus of an atom is equal to the number of electrons outside the nucleus. When a body is rubbed with another, due to friction, some electrons from one body gets transferred to the other body. The body, which loses electrons, will become positively charged and which gains electrons becomes negatively charged. The two bodies thus acquire opposite charges and they are equal in magnitude. This is the reason for frictional electricity.
Gold Leaf Electroscope:-
*A simple apparatus to detect charge on a body is called a gold-leaf electroscope.
* Apparatus It consists of a vertical metal rod placed in a box. Two thin gold leaves are attached to its bottom end as shown in figure.
WORKING:-
When a charged object touches the metal knob at the top of the rod, charge flows on to the leaves and they diverge. The degree of divergence is an indicator of the amount of charge
Conductors and Insulators:-
CONDUCTORS:
Conductors are those substances which allow passage of electricity through them.
Eg. Metals, human and animal bodies and earth are conductors.
• They have electric charges (electrons) that are comparatively free to move inside the material.
• When some charge is transferred to a conductor, it readily gets distributed over the entire surface of the conductor.
▪ Metals cannot be charged by friction,because the charges transferred to the metal leak through our body to the ground as both are conductors of electricity.
Insulators:-
The substances which offer high resistance to the passage of electricity through them are called Insulators .
Eg. glass, porcelain, plastic, nylon, wood
▪ If some charge is put on an insulator, it stays at the same place. So insulators gets electrified on combing dry hair or on rubbing,
Earthing (or) Grounding
When a charged body is brought in contact with earth, all the excess charge pass to the earth through the connecting conductor. This process of sharing the charges with the earth is called grounding or earthing. Earthing provides protection to electrical circuits and appliances.
METHODS OF CHARGING:-
A body can be charged in different ways;
1)Charging by friction
2)Charging by conduction
3)Charging by induction
1) Charging by friction
*When two bodies are rubbed each other, electrons in one body (in which electrons are held less tightly) transferred to second body (in which electrons are held more tightly)
*When a glass rod is rubbed with silk, some of the electrons from the glass are transferred to silk. Hence glass rod gets +ve charge and silk gets -ve charge.
2) Charging by conduction;
Charging a body with actual contact of another body is called charging by conduction. If a neutral conducting body (A) is brought in contact with positively charged conducting body (B), the neutral body gets positively charged.
3)Charging by induction;
When a charged body is brought near to an uncharged conductor (without touching), that end of the uncharged conductor which is near to the charged body gets oppositely charged and the farther end is charge.
CHARGING A METAL SPHERE POSITIVELY WITHOUT TOUCHING IT:-
Properties of electric charges:-
1.Electric charges are of two kinds – positive and negative.
2.Like charges repel and unlike charges attract each other.
3. Quantization of charge : According to quantization of electric charge, charge of a body is an integral multiple of a basic charge, which is the electronic charge.
Charge on a body, q=± ne ; where, n=1,2,3...…
e is the electronic charge. e=1.602 x 10−19 C.
4.Charge is conserved: It means that total charge of an isolated system remains constant. It also implies that electric charges can neither be created nor destroyed. If an object loses some charge, an equal amount of charge appears somewhere else.
5.Charge is a scalar quantity.
6. Additivity of charge: The total charge on a surface is the algebraic sum of individual charges present on that surface.
If q1, q2 , q3...…, qn are the charges on a surface, then total or net charge,
𝒒 = 𝒒𝟏 + 𝒒𝟐 + 𝒒𝟑 +...… + 𝒒𝒏
(Q)How many electronic charges form 1 C of charge?
ANS: q=±ne,
n= 𝑞/e
n=1/ 1.602 x 10^19
=6.25 x1018
(Q) A comb drawn through person’s hair causes 1022 electrons to leave the person’s hair and stick to the comb. Calculate the charge carried by the comb.
ANS: q= ne,
q = 1022 x 1.602 x 10^19C
= −1.602 x 10^3 C
As the comb gains electrons it gets negatively charged.
COULOMB'S LAW:-
*The force of attraction or repulsion between two stationary electric charges is directly proportional to the product of the charge and inversely proportional to the square of the distance between them.
*Force between two stationary charges in free space;
*if the charges are placed in a medium 
DEFINITION OF COULUMB:-
*When q1=q2=1C,r=1m,F=1/𝜋ε0 = ×10^9 N
*1C is the charge that when placed at a distance of 1m from another charge
of the same magnitude in vacuum experiences an electrical force of repulsion
of magnitude 9 ×10^9 N
Super position principle:-
Force on a charge due to a number of charges is the vector sum of forces due to individual charges.For a system of n charges.
Electric Field:-
*Electric field is the region around a charge where its effect can be felt. Intensity of electric field at a point is the force per unit charge.
E=F/q
F=qE
Unit of electric feild is N/C or V/m
It is a vector quantity
Electric field due to a point charge:-
Electric field due to a system of charges:-
Electric field at a point due to a system of charges is the vector sum of the electric fields at the point due to individual charges
Electric Field Lines:-
An electric field line is a curve drawn in such a way that the tangent to it at each point is in the direction of the net field at that point.
▪ Electric Field lines tart from positive charge, end at negative charge.
▪ Electric field lines of a positive charge are radially outwards and that of a negative charge is radially inwards
▪ Electric field lines do not form closed loops.
▪ In a charge free region field lines are continuous.
▪ Two field lines never intersect.( Two directions for electric field is not possible at a point)
▪ Field lines are parallel ,equidistant and in same direction in uniform electric field.
ELECTRIC FLUX:-
𝛟 = ∫ 𝐄 ⋅ds
𝛟 = ∫ 𝐄 ⅆ𝐒 𝐜𝐨𝐬 θ
*Unit-Nm^2/C
*It is a scalar quantity
Electric Dipole:-
An electric dipole is a pair of equal and opposite charges separated by a distance
Electric Dipole moment (𝐩⃗ ):-
*Electric Dipole moment(p) is the product of magnitude of one the charges and the distance between charges.
*p=q×2a
*q - magnitude of charge
*2a - distance between the charge or dipole length
*Unit of dipole moment in Cm
*Dipole moment is a vector quantity
*Dipole moment is directed from the negative charge to the positive charge
along the dipole axis.
PHYSICAL SIGNIFICANCE OF ELECTRIC DIPOLE:-
Non Polar molecules
*In non-polar molecules the centers of positive charges and negative charges lie at the same
place.
8Dipole moment is zero for a non polar molecule in the absence of an external field.
8They develop a dipole moment when an electric field is applied
Eg: CO2,CH4
Polar molecules
The molecules in which the centres of negative charges and of positive charges
do not coincide Therefore they have a permanent electric dipole moment,evenin
the absence of
an electric field
Eg:water(H2O)
Electric Field duo to a Dipole along the Axial Line:-
The electric field at P due to +q
𝐸+𝑞 = 1/ 4𝜋𝜀0 𝑞/ (𝑟−𝑎) 2 (in the direction of dipole moment 𝑝) The electric field at Pdue to -q
𝐸−𝑞 = 1/ 4𝜋𝜀0 𝑞 /(𝑟+𝑎) 2 (opposite to the direction of dipole moment 𝑝 )
Toal field, E =𝐸+𝑞 − 𝐸−𝑞
𝐸 = 1/ 4𝜋𝜀0 𝑞 /(𝑟−𝑎) 2 − 1/ 4𝜋𝜀0 𝑞/ (𝑟+𝑎) 2
Thus the total electric field at P is
𝐸 = 𝑞 /4𝜋𝜀0 [ 1/ (𝑟−𝑎) 2 − 1/ (𝑟+𝑎) 2 ]
Simplifying
𝐸 = 𝑞/ 4𝜋𝜀0 [ 4𝑎𝑟 /(𝑟 2−𝑎2) 2 ]
For r≫ 𝑎 ,we get
𝐸 = 1 /4𝜋𝜀0 [ 4𝑞𝑎/ 𝑟 3 ]
2qa=𝑝 (dipole moment)
Electric Field duo to a Dipole along the Equatorial Line:-
The magnitude of electric field at P due to +q
𝐸+𝑞 = 1/ 4𝜋𝜀0 𝑞 /𝑟 2+ 𝑎2 ----------------(1)
The magnitude of electric field at P due to -q
𝐸−𝑞 = 1 /4𝜋𝜀0 𝑞 /𝑟 2+ 𝑎2 ------------------(2)
The vertical components cancel each other and horizontal components add up
Total electric field at P,
E =𝐸+𝑞𝑐𝑜𝑠𝜃 + 𝐸−𝑞𝑐𝑜𝑠𝜃
But , 𝐸+𝑞 = 𝐸−𝑞
E =2𝐸+𝑞𝑐𝑜𝑠𝜃 --------------(3)
Cos𝜃= 𝑎 /√𝑟 2+𝑎2 = 𝑎 /(𝑟 2+𝑎2) ^1/ 2 ⁄ ----------(4)
Substituting eq(1) and (4) in eq(3)
E =2 𝑥 1/4𝜋𝜀0 𝑞 /𝑟 ^2+ 𝑎^2 𝑥 𝑎 /(𝑟 ^2+𝑎^2) 1/ 2
p=2qa (dipole moment)
𝐸 = 1/ 4𝜋𝜀0 [ 𝑝 /(𝑟^ 2+𝑎^2) 3/2 ]
For r≫ 𝑎 ,we get
𝑬⃗ = 𝟏 /𝟒𝝅𝜺𝟎 [ 𝒑⃗ /𝒓 𝟑 ]
Relation connecting Axial field and Equatorial field of a Dipole:-
Axial field, 𝐸⃗ = 1/ 4𝜋𝜀0 [ 2𝑝/ 𝑟 3 ]
Equatorial field , 𝐸⃗ = 1/ 4𝜋𝜀0 [ 𝑝 /𝑟 ^3 ]
Axial field = 2 x Equatorial field
Dipole in a Uniform External field:-
In a uniform electric field there will be a net torque on the dipole, but the net force will be zero. Due to the torque ,the dipole rotates. There will be no translatory motion as the net force is zero.
Torque on a Dipole in a Uniform External field:-
Torque, τ = one of the forces x perpendicular distance between them.
τ = qE x 2a sinθ
τ =pE sinθ
𝛕 = 𝐏⃗ × 𝐄⃗
• When p and E are in the same direction or opposite direction( θ=0 or180 )
τ =pE sin0 =0
• Torque is maximum , when p and E are perpendicular. (θ=90)
τ =pE sin90 =pE
Dipole in a non uniform electric field:-
In a non uniform electric field the dipole experiences a net force as well as a net torque in general .
But the net torque will be zero τ =pE sin0 =0
Case 2-When p is antiparallel to E.
When p is antiparallel to E, the net force on the dipole is in the direction of decreasing field. But the net torque will be zero, τ =pE sin 180 =0
Continuous Charge Distribution:-
Linear charge density
The linear charge density λ of a wire is defined as
𝜆 = 𝛥𝑞/𝛥𝑙
𝝀 = 𝒒/𝒍
The unit of λ is C/m
Line charge q = 𝝀𝒍
Surface charge density
𝜎 = 𝛥𝑞 /𝛥𝑆
𝝈 = 𝒒/ 𝑺
The units for σ is C/𝑚2
Surface charge, q= 𝝈𝑺
Volume charge density
ρ = 𝛥𝑞/ 𝛥𝑉
𝛒 = 𝒒 /𝑽
The units for ρ is C/𝑚3
Volume charge , q= 𝛒𝑽
Gauss’s Theorem:-
Gauss’s theorem states that the total electric flux through a closed surface is equal to 𝟏 𝜺𝟎 times the total charge enclosed by the surface.
𝝓 = ∮ 𝑬 ⋅ ⅆ𝑺 = 𝒒 𝜺𝟎
The surface over which we calculate the flux is called Gaussian surface
Proof:-
Consider a sphere of radius r enclosing a point charge q.
The electric flux through the surface ds
Features of Gauss's law
*Gauss's law is true for any closed surface irrespective of the size and shape.
*The charge includes sum of all charges enclosed by surface.
*Gauss's law is useful to calculate electric field when the system has some symmetry.
*Gauss's law is based on the inverse square dependence on distance contained in the
Coulomb's law.
Applications of Gauss's law
1)Electric field due to an infinitely long straight uniformly charged wire
To find the electric field at point P at distance r consider cylindrical Gaussian surface of radius r
2)Electric filed due to a uniformly charged infinite planesheet
3)Electric field due to a uniformly charged thin spherical shell
a)Filed outside the shell
b)filed on the surface of the shell
c)field Inside the shell
Example
Find the electric field due two plane sheets of charge in regions I ,II and II
