Electric field 2

Dipole :- When two equal and opposite charge placed at very small distance then this formation is called dipole and distance between them is 2a.
here 2a = 1Å (One Angstrom ) = 10^-10 meter

Let two charges +q and -q are formed a dipole so

Dipole momentum :- It is the product of one charge of dipole and distance between them. It is denoted by 'p'.
p = 2*q = 2aq
It's unit is coulomb*meter (c*m).

Electric field due to a dipole :- There are two conditions to find electric field intensity due to a dipole -
1. Electric field intensity at axis of dipole :-
Let a dipole AB. A positive charge +q0 is present at point p at r distance from center of dipole O.

distance of p from +q is (r-a) and from -q (r+a) so
electric field intensity at p due to +q
E1 = kq / (r-a)^2          ....(1)
electric field intensity at p due to -q
E2 = kq / (r+a)^2         ....(2)
so total electric field intensity at p due to dipole
E = E1 - E2
E = [kq / (r-a)^2] - [kq / (r+a)^2]
E = kq [1 / (r-a)^2 - 1 / (r+a)^2]
E = kq [{(r+a)^2-(r-a)^2} / {(r-a)^2(r+a)^2}]
E = kq [{(r^2+a^2+2ar) - (r^2+a^2-2ar)} /  {(r-a)(r+a)}^2]
E = kq [(r^2+a^2+2ar - r^2-a^2+2ar) / (r^2 - a^2)^2}
E = kq [4ar / (r^2-a^2)^2}
since r >> a then r^2 >>>> a^2 so neglecting a^2
E = k [2*2aq*r / (r^2)^2]
since 2aq = p (dipole momentum )
E = 2kpr / r^4
E = 2kp / r^3                ....(3)
It is the electric field intensity at axis of dipole.
Here k = 1 / 4πε0  = 9*10^9 Nm^2/c^2

2. Electric field intensity at equator of dipole :-
 Let a dipole AB. A positive charge +q0 is present at r distance from mid point 'o' of dipole at point p.

now connect point A&B to P so AP & BP are hypotenuse so AP = BP = {(r^2+a^2)}^1/2so electric field intensity at p due to +q
E1 = kq / {(r^2+a^2)^1/2}^2
E1 = kq / (r^2+a^2)       ....(1)
electric field intensity at p due to -q
E2 = kq / (r^2+a^2)       ....(2)
here from equations (1) &  (2)
E1 = E2
so they cancel each other means E = 0 which is not possible.
so E1 & E2 are divide into components
E1 Sinθ & E2 Sinθ are equal and opposite so they cancel each other and E1 Cosθ & E2 Cosθ are in same direction so they add.
so resultant electric field intensity is given by
E = E1 Cosθ + E2 Cosθ
E = 2E1 Cosθ               ....(3)  
From triangle PBO
Cosθ = BO / BP
Cosθ = a / (r^2+a^2)^1/2  ....(4)
so again from (3)
E = 2[ {kq / (r^2+a^2)}{a / (r^2+a^2)^1/2}]
E = 2[kqa / (r^2+a^2)^3/2]
since 2aq = p (dipole momentum)
so E = kp / (r^2+a^2)^3/2
since r >>a so r^2 >>>> a^2 neglecting a^2
E = kp / (r^2)^3/2
E = kp / r^3        ....(5)
It is the electric field intensity at equator of dipole.
Here k = 1 / 4πε0  = 9*10^9 Nm^2/c^2

Electric Field 1

Electric field :- It is the area around any charge. When any charge enters in it then that charge feel force ( attraction or repulsion ).

Electric Field Intensity :- The force acting on a unit positive charge is known as electric field intensity.
It is denoted by 'E'.
E = F/q0
here q0 is unit positive charge.
or we can say force per unit charge is known as electric field intensity.
It's unit is newton per coulomb(N/c).

Electric field intensity due to a point charge :-
Let a positive charge +q is present at point 'o' and another charge +q0 present at 'p', r distance from o.

Due to same charge a repulsive force acting
F = kqq0/r^2
when this charge enters into electric field then electric field intensity on it
E = F/q0  ( according to the definition of electric field intensity)
so E = (kqq0/r^2)/q0
    E = kqq0/r^2q0
    E = kq/r^2
here k = 1/4πε0 = 9*10^9 Nm^2/c^2
so E = 1/4πε0(qq0/r^2)

Electric force

To find force between two static charges a law given by scientist Charles-Augustin de Coulomb in 1784. Which is known as Coulomb's law or Coulomb's inverse square law.

Coulomb's law :-
When two point charge present at a distance then force between them is -

1. Directly proportional to product of charge.
2. Inversely proportional to square of distance between them.

Let two point charge q1 and q2 present at a distance r then
F α q1.q2   ........(1)
F α r²         ........(2)
 now from equation (1) and (2)
F α (q1.q2)/r^{2  ......(3)
F = k(q1.q2) /}r2 N
here k is coulomb's constant.
k = 1/4πε₀  = 9*10^9 Nm^2/c^2
here N = Newton ( unit of force)
ε₀  is permittivity of vacuum = 8.85*10^-12 c^2/N.m^2
Permittivity of vacuum:- It is the capability of vacuum to flow the charges.

Note:-

• Coulomb's force is applicable only for static charge.
• It is applicable for point charges.
• It is low range force.

Point charge:- Charges whose size are very smaller then distance between them called point charge.

Electric charge

Electric current:- It is the flow of charge.
Charge :- We know that every material is formed by molecules, molecules by atoms. It every atom neutron,proton,electrons are present. Electron is a moving particle.Which is responsible for charge.

• It is denoted by 'q','Q'.
• It's unit is coulomb (c).

It has two types-
Positive charge- It is due to deficiency of electrons.

Negative charge- It is due to excess of electrons.

NOTE-  In every atom number of electron = number of proton
means atom is neutral (Charge is zero).
When electron emits from it then number of proton > number of electron. Means it is positively charged.
When electron receive by atom then number of proton < number of electron. Means it is negatively charged.
Since electron is negatively charged and proton is positively charged.

Electric current is discovered by German scientist Benjamin Franklin.
According to them when a glass rod is rubbed on silk cloth then electron from rod transfer to silk.due to it rod become positive and silk cloth negative. Like that when ebonite rod is rubbed on fur then electrons from fur transfer to rod. Due to it fur become positive and rod negative.

Force between charges:-
When positive charged rod is freely suspended and another same positive charged rod taken near to it then suspended rod moves upward. Means same charge repel each other.
When positive charged rod is freely suspended and negative charged ebonite rod taken near to it then suspended rod moves downward. Means opposite charge attract each other.

+ and +, - and -repel
+ and - attract

Properties of charge:-
1. Quantization of charge :- The total charge of any conductor is intiger multiplier of number of electron present on it.
q = ne
here q charge of conductor
n = intiger numbers 0,1,2,3,4............n
e = charge of electron 

1.60217662 × 10^-19 coulombs

1.6 × 10^-19 coulombs (approx).

2. Additive :- When multiple charge present on any conductor then total charge of that conductor is algebric sum of all present charges.

q = q1 + q2 + q3 +........ qn

3. Conservation of charge :- Like energy, charge is neither be created nor be destroyed. It only transfer from one conductor to another. Means total charge charge of conductor is conserved.

Energy

Energy :- It is the capacity or ability of work done by a body.

• It is a scalar quantity.
• Its unit is joule and dimension is [M^1L^2T^-2].
• It has following types-

1. Internal Energy - It is the energy of system due to its atom or molecules.
2. Mechanical Energy - It is the sum of kinetic and mechanical energy of system.
   
   
   
   
   
   
3. Sound Energy - It generate the sensitivity in ear drums. It is required to listen voice.
4. Light Energy - It generate the sensitivity in eyes. It is required to watch object.
5. Electrical Energy - It is due to flow of electrons in any conductor.
6. Solar Energy - It is obtain from Sun light.
7. Chemical Energy - It is generate due to chemical reactions.
8. Nuclear Energy - It is due to nuclear reactions like Nuclear fission (Atom Bomb), Nuclear fusion (Hydrogen Bomb).
9. Thermal Energy - It is due to heat (temperature)  of any object.
10. Gravitational Energy - It is the work done by earth to attract any object.

Kinetic Energy - It is due to motion of body (object).
example - Wind mills work on the kinetic energy of air.

Let an object of mass m is in rest(initial velocity u=0). When F force applied on it then it accelerated by a with velocity v and displacement s.
by using third equation of motion
v^2-u^2 = 2as
since u = 0
so v^2 = 2as
a = v^2/2s
since F = ma
so F = mv^2/2s
and work W = F.s
W =  (mv^2/2s).s
W = mv^2/2
This work is stored as kinetic energy.
so K.E. of body = mv^2/2

Potential Energy - It is due to position of object.
example - Chemical energy from a bettery.
                Energy of a body placed at a height from earth surface.

Let an object of mass m is placed at h height from earth.
force F = mg ( here a = g gravitational acceleration )
work W = F.h
so W = mgh
This work is stored as potential energy.
P.E. of body = mgh

WORK

Work is a process by which displacement generate in any object by applying a force on it.
It is the scalar product of force and displacement.
If 'd' displacement generated by force 'F' then the total work done -
W = F.d = Fd Cosθ
here θ is the angle formed between force and displacement.

• If θ is 0 means force and displacement in same direction then the work  W = Fd (maximum)  (cos0=1).
• If θ is 90 means force and displacement perpendicular to each other then the work  W =0 (minimum) (cos90=0).

• If there is no any displacement by force the applied work done 'zero'. Like a person pushing a wall.

• In a circular motion total work done is zero because there is no any displacement in circular path.
• Its unit is Newton*meter = joule  (N.m = J).
• 1J = 1N.1m 
• When one newton force applied on a body and it displaced by one meter then the work done is one joule.
• Dimension is [M^1L^2T^-2].
• In the form of derivative  dW = F.ds = FdS Cosθ.

Force

'To push' or 'Pull' any object is called force. Means it creates change in position of any object.

Properties of force -

1. It will be in point form.
2. Due to force the shape, size and mass will change.
3. No any contact required for apply force.
4. When multiple force applied on any object. Object is in rest then it is condition of equilibrium. In this condition total force on object is zero.
5. When multiple force applied on any object. Object is not in rest then it is condition of non-equilibrium. Object moves in the direction of resulting force.
6. When force applied perpendicular to the direction of motion of object. Object moves in elliptical path.
7. When force applied perpendicular to the direction of motion of object at every point of motion. Object moves in circular path.

Fundamental forces are following -

1. Gravitational force - Every object which have mass attract another object of mass.
It is the weakest force in nature. 

Its range is very high.
It is given by Newton.
According to Newton's universal law of gravity - "The force between two objects is directly proportional to product of their masses and inversely proportional to square of distance between them.
If two objects of masses M1 & M2 placed R distance apart then
F ∝ M1 M2
F ∝ 1/R^2
F ∝ (M1 M2)/R^2
So F = G(M1 M2)/R^2
Unit of force is Newton, denoted by N.
Here G is gravitational constant.

G = F.R^2/(M1 M2)
  =N.m^2/kg^2
For earth G= 6.67*10^(-11) Nm^2/kg^2

2. Electromagnetic force - When constant electric current flow in circuit then magnetic field generate around it.

It is second strongest force in nature.

3. Strong nuclear force - It is applied between nucleons(neutron, proton). It is high attracting force which bind nucleons.
It is the strongest force in nature.

4. Weak nuclear force - It is due to ß decay from nucleus. Then that nucleus attract nearby nucleus.

Motion

Motion - It is the change of position of object with respect to time.

It has following types -

1. Translatory motion - Object moves along a straight line.
Motion of car,bus etc.

2. Rotational motion - Object moves around any fix axis. And that fix axis is known as axis of rotation.
Motion of object in a circular path. Radius of that circle is axis of rotation or rotational axis.

3. Oscillatory motion - Object moves up-down, left-right, to-fro of its mean position.
Motion of loaded spring, to make swing, pendulum etc.

Note- In the absence of any external force object is placed at a position which is known as mean position.
Example.-When cell of clock is taken out then its pendulum is in rest at a position. which is mean position.

Types of motion on the basis of dimensions.

It has following types -

1. One dimensional motion - Object moving along a particular axis(x, y or z).

Motion of car bus, human.

2. Two dimensional motion - Object moving in a plane (xy, yz, zx).
Motion of a fly.

3. Three dimensional motion - Object moving in free space.
Motion of Bird, Airplane etc

.

Definition related to motion

Position - A place, coordinate, point where any object placed.
If any object change its position then it has two positions - Initial position & Final position.

Distance-The difference of final and initial position. It is denoted by 'd'. It is a scalar quantity.

Displacement - The distance in a particular direction. It is the minimum distance between initial and final positions. It is denoted by x. It is a vector quantity.

 Speed- It is the rate of change of distance.
    v =d/t
It is a scalar quantity.

Velocity - It is the rate of change of displacement.
     v = x/t
It is a vector quantity.

Acceleration - It is the rate of change of velocity.
         a = v/t
It is a vector quantity.

Note:-
1. Scalar quantity - The physical quantities which have only magnitude no any direction.
Distance, temperatures, pressure, speed, work, energy etc.
2. Vector quantity - The physical qualities which have both magnitude and direction.
Displacement, velocity, acceleration, force etc.
3. Tensor quantity - The physical qualities which behave as both scalar and vector quantities.
Angular velocity, angular acceleration, angular moment etc.

Physics

'Physics' word is taken from Greek word 'Fusis'. Which means 'Nature'.
Physics is the branch of science in which we study about nature, natural principles, natural phenomenons.
Physics has two types -
(A) Classical physics - It is the knowledge of physics before 19th century.
It has following types -
1. Machines
(a) statics
(b) dynamic
(c) fluid motion
(d) aerodynamic
2. Electromagnetic
3. Thermodynamics
4. Wave motion
5. Optics etc.

(B) Modern physics - It is the knowledge of physics after 19th century.
In 1919 German scientist Max plank gave Quantum Theory.
According to quantum theory "light travel in the form of small packets of energy which know as quanta or photon". The rest mass of photon is zero so gravity doesn't apply to them.
On the basis of this theory so many changes are occurred in physics and that changes are called modern physics.
It has following types -
1. Solid state physics
2. Molecular physics
3. Atomic physics
4. Nuclear physics
5. Plasma physics
6. Quantum physics etc.