PHYSICS in our life..!!

PHYSICS➨PART- 1

Nothing happens until something moves

Well this session consists of  PHYSICS .  This part consist Physical constant and formulae . I tries to tell ,in such a way as to be understood by everyone.The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.

Physical Constants

1 - Average acceleration of gravity (g) →                9.81 m/s²
2 - Gravitational constant (G) →                             6.67× 10 ⁻ ¹¹ Nm²/kg²
3 - Mass of electron (mₑ ) →                                     9.11 × 10 ⁻³¹ kg = 0.511 MeV/c²
4 - Mass of proton (mₚ ) →                                      1.673 × 10 ⁻²⁷ Kg = 1.007 u
                                                                                   = 938.3 MeV/c²
5 - Mass of neutron (mₙ ) →                                   1.657 × 10 ⁻²⁷ Kg = 1.009 u
                                                                                = 939.6 MeV/c²  
6 - Speed of light in vaccum ( c) →                       3.00 × 10 ⁸ m/s
7 - Universal gas constant ( R ) →                         8.31 J/mol K
8 - Boltzmann constant ( kʙ ) →                           1.38 × 10⁻²³ J/k
9 - Avogadro constant (Nᴀ) →                              6.02 × 10 ²³ / mol
10 - Permittivity constant ( ∈₀ ) →                       8.85 ×  10⁻¹²  C²/Nm² = 8.85 pF/m
11 - Coulomb constant or
      Electric constant ( kₑ ) →                                1/4 𝝅∈₀ = 8.99 × 10⁹ Nm²/C²
12 - Elementary charge ( e ) →                           1.60 × 10 ⁻¹⁹ c
13 - Permeability constant ( μ₀ ) →                      4𝝅× 10⁻⁷ Tm/A = 1.26 × 10 ⁻⁶ N/A²
14 - Magnetic constant ( kₘ = μ₀ /4𝝅 ) →             10⁻⁷ Tm/A
15 - Planck constant ( h ) →                                 6.63 × 10 ⁻³⁴ Js = 4.14 × 10 ⁻¹⁵ eVs
16 - Bohr radius ( r₀ ) →                                       5.29 × 10⁻¹¹ m = 0.529 Å
17 - Electron volt ( eV ) →                                    1.60 × 10⁻¹⁹ J
18 - Unified atomic mass unit ( amu) ( n) →       1.66 × 10⁻²⁷ Kg
19 - Rydberg constant ( R ) →                             1.097 × 10⁷m⁻¹
20 - Bohr magneton (μ ) →                                  9.274 × 10⁻²⁴ J/T

Formulae of Physical Quantities

1 - Quantisation of charge → q = ne   (q is the charge on a body and n is an integer , it can be positive or negative )

2 - Coulomb's law → F = kₑ q₁ q₂/r² ( F is the force in between two charges q₁and q₂ placed in a vacuum at a distance r )

3 - Relative permittivity  Or Dielectric constant → ∈ᵣ = F/Fₘ  ( ∈ᵣ is the relative permittivity of a medium . Fₘ is the force acting between two point charges q₁ and q₂ placed in a medium at the same distance r apart. )

4 - Absolute permittivity → ∈ᵣ = ∈ /∈₀  ( ∈ is absolutely permittivity of a medium )

5 - Electric field intensity → E = F / q₀  ( E is the electric field intensity and F is the force acting on a test charge q₀ placed in the field )

6 - Electric field due to an isolated point charge → E = kₑ q/r²  ( E is the electric field due to an isolated point charge q at a point distant r from q. )

7 - Electric intensity due to an infinitely long thin wire → E = 2kₑλ/x = λ/ 2𝜋∈₀x  ( E is the intensity due to an infinitely long thin wire at a distance x , λ being the linear charge density of the wire.)

8 - Electric intensity due to a conducting ring → E = kₑ qx/ (R²+x²)³/²  ( E is the electric intensity due to a conducting ring of radius R and carrying a charge q at a point lying on it's axis of symmetry at a distance x from it's center .)

9 - Electric dipole moment → p = q × 2a = 2qa ( p is the electric dipole moment of an electric dipole of each charge of magnitude q , placed a distance 2a apart. )

10 - Electric field intensity due to a dipole on its axial line → E (axial) → kₑ2pr/(r²-a²)²
E (axial) → kₑp/r³  ( E axial is the electric field intensity due to a dipole on the axial line at a point distance r from it's center , p being the dipole moment of the dipole.)

11 - Electric field intensity due to a dipole on its equatorial line → E (equatorial ) = kₑp/ (r²+a²)³/²
E (equatorial) = kₑp/r³ (for a short dipole)  (E equatorial is the electric field intensity due to a dipole on its equatorial line at a point distance r from its center , p being the dipole moment of the dipole.)

12 - Electric field intensity  ➝ E= σ/2∊₀ ( E is the electric field intensity due to an infinite uniformly charged plane sheet of surface charge density σ.)

E = σ /∊₀  ( E is the electric field intensity due to an infinite charged conducting plate of surface charge density σ. )

13 - Torque → ꞇ = p × E  Or  ꞇ = pEsin𝜃  (ꞇ is the torque acting on an electric dipole of dipole moment p lying at angle 𝜃 with the electric field E)

14 - Potential energy → U = - p.E ( p and E both are in vector form )= -pEcosθ       (U is the potential energy of an electric dipole of dipole moment p  lying at  an angle θ with the electric field E.)

15 - Work done → W = 2 pE  ( work done to reverse the dipole , that is turning its end for end.)

16 - Electric flux → Φᴇ = EA = q/∊₀   ( Φᴇ is the electric flux through a surface of area A, placed perpendicular to a uniform electric field E.)

17 - Potential difference → Δ V = Vʙ - Vᴀ = Wᴀʙ / q₀  ( ΔV is the potential difference between points A and B and Wᴀʙ is the work done in carrying a positive charge q₀ from A to B.)

18 - Potential gradient → E = - dV/dr  ( dV/dr is called the potential gradient )
E = V/r  ( E is a uniform electric field .)

19 - Potential energy → U = kₑ ( q₁q₂/x₁ + q₂q₃/x₂ + q₃q₁/x₃)   ( U is the potential energy of a configuration of three charges q₁,q₂,and q₃ placed in vacuum .x₁ is the distance between q₁ q₂ ; x₃ is the distance between q₂ q₃ ; x₃ is the distance between q₃ q₁.)

20 - Capacitance of a conductor → C= Q/V ( C is the capacitance of a conductor having charge Q and a potential V.)

21 - Capacitance of a parallel plate conductor → C = ∊₀A /d  ( C is the capacitance of a parallel plate conductor , A is the area of the plates and d is the separation between them.)
[ A capacitor consists of isolated conductors plates carrying equal and opposite charges +Q₁ , and - Q₂ .)

22 - Capacitance of a spherical capacitors →  C = ab/ kₑ(b - a) = 4𝝅∊₀ab/ (b - a)   (C is the capacitance of a spherical capacitor , a is the radius of the inner charged sphere and b that of the outer earthed shell.)

24 - Resultant capacitance in series combination → 1/Cₛ = 1/C₁ + 1/C₂ +1/C₃  (Cₛ is the resultant capacitance in series combination of capacitors of capacitance C₁, C₂, C₃.)

25 - Resultant capacitance in parallel combination → Cₚ = C₁ + C₂ + C₃  ( Cₚ is the resultant capacitance in parallel combination of capacitors of capacitance C₁ ,C₂ and C₃ )

26 - Electric potential energy stored in a capacitor → U = 1/2CV² = QV/2 = Q²/2C  (U is the electric potential energy stored in a capacitor of capacitance C , having charge Q and at a potential V.)

27 - Energy density → uₑ = 1/2∈₀ E²  ( uₑ is called the energy density that is electric potential energy per unit volume stored in an electric field E.)

28 - Loss of energy → U₁-U₂ = 1/2 (C₁C₂/C₁+C₂)(V₁-V₂)²   ( U₁-U₂ is the loss of energy on sharing the charges ; C₁ and C₂ are the capacitance of two conductors at potential V₁ and V₂.)

29 - Dielectric constant → ∈ᵣ = C/C₀  ( ∈ is the dielectric constant and C and C₀ denote the capacitance of a capacitor with and without dielectric.)

30 - Capacitance of a parallel plate capacitors → C = ∈₀A/ (d-t) + t/∈ᵣ  ( C is the capacitance of a parallel -plate capacitor with a dielectric slab of thickness t between its plates, each of area A and having a separation d.)
C = ∈₀A/d-t  ( C is the capacitance of the parallel - plate capacitor with a conducting slab of thickness t between its plates, each of area A and having a separation d.)

31 - Steady current → I = q/t
Instantaneous current I = dq /dt  ( I is the current due to flow of charge q Or dq through a conductor for a time t Or dt.)

32 - Ohm's Law → V = RI   ( V is the potential difference across the ends of a conductor through which a current I flows . Here R is the resistance of the conductor.)

33 - Conductance → G =1/R = 1/ V  (G is the conductance of a conductor.)

34 - Resistivity → ⍴ = RA/l     =  m/ne²ꞇ     (⍴ is the resistivity of the material .R is the resistance of a conductor of a lenght l , cross sectional area A . n is the number density of electrons , ꞇ is the relaxation time that is mean time between the collision of an electron with the ions of metal lattice , m is the mass of the electron and e its charge.)

35 - Current in terms of drift speed → I = nevdA   ( A is the cross sectional area of a conductor , n is the number density of electrons ( number of electrons per unit volume ) , e is the charge on the electron and vd is the drift speed of the electron when current I flows through the conductor.)

36 - Current density → J = I/A = n e vd  ( J is the current density.)

37 - Electrical conductivity →  σ = 1/⍴ = ne²ꞇ/m   ( σ is electrical conductivity)

38 - Resultant resistance → Rₛ = r₁ +r₂ +r₃   ( Rₛ is the resultant resistance of a number of resistors in series.)
1/Rₚ = 1/r₁ +1/r₂ +1/r₃   ( Rₚ is the resultant resistance of a number of resistors in parallel)

39 - emf of cell → ɛ = dW/dq   (E is the emf of cell and dW is the amount of work that the cell does to force positive charge dq from the negative terminal to the positive terminal.)

40 - Internal resistance → r =(ɛ-V/V)R   ( r is the internal resistance of a cell of emf ɛ and V is the potential difference across the terminals of the source when the current flows through an external resistance R.)

41 - Delivering current → V = ɛ - IR  ( when the cell is  delivering current , that is cell is discharging itself.)

42 - Receiving current → V = ɛ + IR   ( when the cell is receiving current , that is , the cell is being charged .)

43 - Series grouping of cell → I = nɛ / R+nr   ( A number (n) of cells are grouped in series to get maximum current I when the external resistance R is much more than the internal resistance r of each cell .)

44 - Parallel grouping of cells → I = ɛ /(R+r/m)   ( A number (m) of cells are grouped in parallel to get maximum current I when the external resistance R is much less than the internal resistance r of each cell.)


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