JEE Exam » JEE Important Formulas » JEE Physics Important Formulas Part -7

JEE Physics Important Formulas Part -7

In this article, we will go through physics quick formula revision for JEE. Find the important formulas of Wave and Wave Optics, Work Power and Energy, Kinetic Theory and Kinetic Theory of Gases.

Wave Formula

Electromagnetic wave equations are given as below

DescriptionFormula
Gauss’s Law for electricity∮ E.da=Q/ϵ_0
Gauss’s Law for MagnetismB.dA=0
Faraday’s LawE.dl=-dϕdt
Ampere-Maxwell Law∮ B.dl=μ_0 ϵ_0 (dϕ_E)/dt
Speed of Light in Vacuumc=1/√(μ_0 ϵ_o )
Speed of light in mediumv=1/√μϵ
Relation between Electric and Magnetic fieldE_0/B_0 =c

Wave Formula

The formula for wave  are as stated below

DescriptionFormula
General Equation of Wave Motion(∂^2 y)/(∂t^2 )=v^2 (∂^2 y)/(∂x^2 )
Wave number
Phase of a Wave

It is the difference in phases of two particles at any time t.

∆ϕ=2π/λ∆x  

Speed of Transverse Wave Along a String / Wirev=√(T/μ) where T=Tension(-1)

μ=mass per unit length

Power Transmitted Along The String By a Sine Wave

Average Power (P)

P=2π^2 f^2 A^2 μv v =velocity

Intensity

I=P/S=2π^2 f^2 A^2 ρv
Longitudinal Displacement of Sound Waveϵ=A sin⁡(ωt-kx)
Pressure Excess during travelling sound waveP_ex=-B ∂ϵ/∂x=(B) Cos (ωt-kx)

Where B is the Bulk Modulus

Pex is the excess pressure

Speed of Sound C=√(E/ρ)

Here, E is elastic modulus ρ

is the density of medium

Loudness of Sound 10 ( I/I_0 ) dB
Intensity at a distance r from a point SourceI=P/(4πr^2 )
Interference of Sound WaveP_1=P_m1 Sin(ωt-kx_1+θ_1 ) P_2=P_m2 Sin(ωt-kx_2+θ_2)The Result is the sum of all the pressure. P_0=√(p_(m_1)^2+p_(m_2)^2+2p_(m_1 ) P_m2 cosϕ)
For constructive Interferenceϕ=2πn then,=>P_o=P_(m_1 )+P_(m_2 )
For destructive interferenceϕ=(2n+1)π and=>P_o=|P_(m_1 )-P_(m_2 ) |
Close Organ Pipef=v/4l,3v/4l,5v/4l,….((2n+1)v)/4l
Open organ pipef=v/2l,2v/2l,…nV/2l
BeatsBeats Frequency=f1–f2
Doppler’s Law

The Observed Frequency,

f^’=f((v-v_0)/(v-v_s ))

Apparent Wavelength,

λ^’=λ((v-v_s)/v)

Wave Optics Formula

The formula for wave optics are as stated below

DescriptionFormulas
The path difference of two coherent Waves

∆d=d2–d1

∆d is the path difference

The Path difference of two coherent waves: Interference Maximum

∆d=k.λ

∆d is path difference λ

is the wavelength

The path difference of two coherent waves: Interference Minimum∆d=((2.k+1).λ)/2

∆d is path difference λ

is the wave length

Thin-film interference: Constructive (maximum)2ntcos r =(n+1/2)λ

t is film thickness

n is refractive index

r is refraction angle

λ is wave length

Thin-Film interference: destructive (minimum)2ntcosr =nλ

t is film thickness

n is refractive index

r is refraction angle

λ is wave length

Radii of Newton’s Ring

 r=√(k.R.λ)    or    r=√(((2.k+1).R.λ) )/2

r is the radius

R is the radius of curvature

λ is the wavelength

Light Diffractionl=d^2/(4.λ)

I is the distance from obstacle

d is the obstacle size

λ is wavelength

Diffraction grating: maximum (bright stripes)dsinθ =kλ

d is the lattice constant

is the diffraction angle

λ is the wavelength

Diffraction grating (dark stripes)dsinθ =(K+1/2)λ

d is the lattice constant

is the diffraction angle

λ is the wavelength

Work Power and Energy Formula

The formula for work power energy are as stated below

DescriptionFormulas
Work done is given by

W=F×d

F is the force

d is the displacement

Kinetic EnergyK.E=1/2 mv^2

m is the mass of the body.

v is the velocity of the body

Potential Energy

P.E=mgh

m is the mass of the body in kg

h is the height of the body in meters

g is the  acceleration due to gravity

Power

P=W/t

W is the work done by the body

t is the time

P=(F ⃗.(ds) ⃗)/dt=F ⃗.V ⃗
Conservative ForcesF=-du/dr
Work-Energy theoremW_net=∆K

Where

Wnet is the sum of all forces acting on the object

K is the change of kinetic energy

Kinetic Theory Formula

The formula for kinetic theory are as stated below

DescriptionFormula
Boltzmann’s Constantk_B= nR/N

kB = Boltzmann’s constant

R = gas constant

n = number of moles

N = number of particles in one mole 

Total translational Kinetic Energy of GasK.E = 3/2 (nRT)

R = gas constant

n = number of moles

T = absolute temperature

Maxwell distribution law

V_rms>V>V_p

V_rms
= RMS speed

Vp = most probable speed

V = average speed

RMS SpeedV_rms= √(3kt/m) = √(3Rt/M)

R = universal gas constant

T = absolute temperature

M = molar mass

Average Speedv ⃗=√(8kt/πm) = √(8Rt/πM)
Most probable speedv_p=√(2kt/m) = √(2Rt/M)
Pressure of ideal gasp = 1/3 ρ〖v^2〗_rms
Equipartition of energy

For each degree of freedom

K=1/2 k_B T

For f degree of freedom

K=f/2 k_B T

kB = Boltzmann’s constant

T = temperature of gas

Internal Energy

For n moles of an ideal gas, internal energy is given as

U=f/2 (nRT)

Kinetic Theory of Gases Formula

The formula for kinetic theory of gases are as stated below

DescriptionFormulas
Boltzmann’s Constantk_B=nR/N
  •  k_Bis the Boltzmann’s Constant
  • R is the gas Constant
  • n is the Number of Moles
  • N is the Number of Particles in one mole (the Avogadro number)
Total Translational K.E of GasK.E=(3/2)nRT
  • n is the number of moles
  • R is the Universal gas Constant
  • T is the absolute Temperature
Maxwell Distribution LawV_rms>V>Vp
  • V_rms is the RMS speed
  • V is the Average Speed.
  • Vp is the most probable speed
RMS Speed (Vrms)V_rms=√(8kt/m)=√(3RT/M)
  • R is the universal gas constant.
  • T is the absolute temperature.
  • M is the molar mass.
Average Speedv ⃗=√(8kt/πm)=√(8RT/πM)
Most Probable Speed (Vp )V_p=√(2kt/m)=√(2RT/M)
The Pressure of Ideal GasP=1/3 V_rms^2
  • P is the density of molecules
Equipartition of Energy

 K=1/2 K_B T  for each degree of freedom

 K=(f/2) K_B T
for molecules having f degrees of freedom

  • KB is the Boltzmann’s Constant
  • T is the Temperature of the gas
Internal EnergyU=(f/2)nRT
  • For n moles of an ideal Gas.

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