Physics Formulas For JEE Mains - Complete List of Most Important Formulas!

JEE Main and JEE Advanced are the two mountains one needs to climb to get to a top technical institute like the IITs or the NITs. Physics is a crucial part of the IIT JEE, with a ton of formulas and brain-aching concepts, it becomes a challenge for all JEE candidates. However, if you organize all the Physics Formulas For JEE Mains topic-wise, you can now see a more clear picture.

This is what we do for you, Testbook brings to you a collection of well-organized formulas for JEE Main Physics formulas.

What is the importance of Physics Formulas For JEE Mains?

Physics becomes an essential part of the JEE preparation, Physics has a balanced mixture of both Theory and Numericals and Solve-the-Equation type of questions occupies the majority part in JEE Physics, hence a list of formulas is required as an aid for your JEE preparation.

Keeping all the Physics formulas at your fingertips helps a lot and saves a lot of time and effort.

It is observed that many of the JEE Main Physics questions are formula-based, if you know the formulas, just plug in the values and a couple of minutes of correct calculations will fetch you a higher rank.

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Overview of the JEE Formulas Physics

Chemistry is an elevator to the gate of IIT but the gate can only be opened through Physics and Maths. Everywhere you look around, you see a lot of Physics. The falling rains, the opening of a book, pulling a chair, switching on the fan, propulsion of a rocket, and whatnot, just take a quick look around you, and you see Physics.

Considering the importance of Physics in our day-to-day life, it is included in the JEE examination and to guide you through these tough times of JEE preparation, Testbook has gathered all the important Physics formulas that a serious JEE candidate must keep in his/her study desk.

The entire syllabus of JEE Physics is categorised under 21 topics, this is done in order to make things more clean and clear, also we understand better if everything is well organised.

These 21 topics are -

1. Vectors
2. Kinematics
3. Newton’s Laws of Motion
4. Work, Energy and Power
5. Circular Motion
6. Center of Mass
7. Rotational Motion
8. Gravitation
9. Solid Mechanics
10. Fluid Mechanics
11. Thermal Physics and Thermodynamics
12. Oscillations and Waves
13. Electrostatics
14. Capacitance and Capacitors
15. Current Electricity
16. Magnetic Effects of Current and Magnetism
17. Electromagnetic Induction
18. Alternating Current and EM Waves
19. Ray Optics and Wave Optics
20. Modern Physics
21. Semiconductors and Communication System

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Topic - 1: Vectors

• The Resultant Vector is written as R=A+B or R=k=1nAk
• The Resultant Vector in Cartesian Form is R=A2+B2+2AB where is the angle between the two vectors.
• If A=Axi+Ayj+Azk then the Direction Cosines are =Ax/A, =Ay/A and =Az/A
• Dot Product: AB=AB where is the angle between the two vectors
• If A=Axi+Ayj+Azk and B=Bxi+Byj+Bzk then the Dot-Product is AB=AxBx+AyBy+AzBz
• Cross Product: AB=AB n where n is a Unit Vector perpendicular to both A and B
• If A=Axi+Ayj+Azk and B=Bxi+Byj+Bzk then the Cross-Product is given by the Determinant

• ij=k, jk=i and ki=j

Topic - 2: Kinematics

• v=dr/dt and a=dv/dt and a=d2r/dt2
• For 1-D Motion: a=v(dv/dx)
• v=u+at, s=ut+(1/2)at2 and v2=u2+2as
• sn-sn-1=u+(a/2)(2n-1)
• v (relative)=v (actual)-v (reference)
• Projectile Motion Initial Horizontal Velocity is ux=u
• Projectile Motion Initial Vertical Motion is uy=u
• Velocity at any instant of a Projectile Motion is v=u i+(u-gt) j
• Horizontal Distance at any time is x=ut
• Time of Flight is T=2u/g
• Maximum Height of the Projectile is H=u22/2g
• Horizontal Range is R=u22/g
• Equation of Trajectory is y=x-gx2/( 2u22 )
• Time of Flight for the Horizontal Projection from a cliff is T=2h/g
• Horizontal Range for the Horizontal Projectile from a cliff is R=uT
• Angle of velocity at any instant for Horizontal Projection from a cliff is =(gt/u)

Topic - 3: Laws of Motion and Friction

• Fundamental Forces of Nature are Gravitational Force, Electromagnetic Force, Weak Nuclear Force and Strong Nuclear Force.
• F=dp/dt and F=ma is mass is constant
• Impulse j=Ft in discrete case and j=t1t2F dt
• Acceleration of Pulley when both masses are downwards is a=| m1-m2 |g/( m1+m2 )
• Tension in the string of a Pulley System when masses are downwards is T=2m1m2g/( m1+m2 )
• Man in a lift going upwards: Fnet=m(g+a)
• Man in a lift going upwards: Fnet=m(g-a)
• Centripetal Force is F=mv2/r=m2r
• Static Frictional Force is f=sN where N is the Normal Force on the object
• Kinetic Frictional Force is f=kN where N is the Normal Force on the object
• Angle of Friction is
• Block sliding on an incline with angle of Repose : f=mg and N=mg

Topic - 4: Work Power and Energy

• Work Done W=Fd when distance is non-variable and W=abFs when distance is variable
• Kinetic Energy K=mv2/2
• Potential Energy U=mgh+h where h is the height from the reference line
• Conservative Force F= -U, in 1-D, it is F= -dU/dx
• Work Energy Theorem: W (all forces)=K=Kf-Ki
• Power P=Fv or P=W/t

Topic - 5: Circular Motion

• Time Period T=1/f is reciprocal of Frequency
• =l/r, =d/dt=2/T=2f and =d/dt
• =v/r or v=r
• Net acceleration a=r+v and a=( 2r )2+( r )2
• Maximum velocity without skidding is v=Rg
• Maximum velocity for banked road is v= (+1- )Rg
• Bending of a Cyclist: vr*g*tan
• Condition to complete the vertical circle is u5gR
• Condition for Oscillation is u2gR and the Tension in the string is T=mg+mv2/R
• Condition for leaving path is 2gR<u<5gR

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Topic - 6: Center of Mass

• The Center of Mass along the x-axis is XCM=(1/M)i=1nmixi where M is the total mass
• The Center of Mass along the y-axis is YCM=(1/M)i=1nmiyi where M is the total mass
• The Center of Mass along the z-axis is ZCM=(1/M)i=1nmizi where M is the total mass
• The Center of Mass for Continuous Distribution is RCM=(1/M)r dm
• If the total mass is M and a small part of mass m is removed then the Center of Mass is given by XCM=(Mx-m)/(M-m), YCM=(My-m)/(M-m) and ZCM=(Mz-m)/(M-m)
• The Center of Mass when the object is moving with some velocity is vCM=(1/M)i=1nmivi
• The Center of Mass when the object is moving with some acceleration is aCM=(1/M)i=1nmiai
• Coefficient of Restitution is e=(v2-v1)(u1-u2)
• Law of Conservation of Linear Momentum: i=1nmiui=j=1nmjvj
• Loss of Kinetic Energy in inelastic collision is K=(1/2M)[ m1m2(1-e2)(u1-u2)2 ]
• Law of Conservation of Linear Momentum for Oblique Collision is i=1nmiui=j=1nmjvj
• Thrust Force on a Rocket is vr(-dm/dt)
• Velocity of a Rocket at any time is v=u-gt+v1(m0/m)

Topic - 7: Rotational Motion

• Angular Momentum L=rp=I where I is the Moment of Inertia
• Torque =rF=dL/dt
• Rotational Kinetic Energy K=I2/2=L2/2I
• Rotational Power P=
• Equations of Motion are =0+t, =0t+t2/2 and 2=02+2
• The nth angular displacement is n-n-1=0+(2n-1)/2
• Moment of Inertia I=i=1nmiri2 in discrete case and I=r2 dm
• Radius of Gyration is k=I/M
• Parallel Axis Theorem Iaxis=ICM+Md2
• Perpendicular Axis Theorem Iz=Ix+Iy
• Moment of Inertia of some common objects -
  • Rod of mass M and length L along its center I=ML2/12
  • Rod of mass M and length L along its corner I=ML2/3
  • Rectangular Lamina of mass M, length L and width W along its width I=ML2/12
  • Rectangular Lamina of mass M, length L and width W along its length I=MW2/12
  • Rectangular Lamina of mass M, length L and width W along its center I=M(L2+W2)/12
  • Ring of radius R along a normal to the plane passing through the center I=MR2
  • Disc of radius R along a normal to the plane passing through the center I=MR2/2
  • Circular Hollow Disc of inner radius r and outer radius R along a normal to the plane passing through the center I=M(r2+R2)/2
  • Hollow Cylinder of radius R along its length passing through the center I=MR2
  • Hollow Cylinder of length L and radius R along the normal to its length and passing through the center I=M(L2+6R2)/12
  • Solid Cylinder of radius R along its length I=MR2/2
  • Solid Cylinder of length L and radius R along the normal to its length and passing through the center I=M(L2+3R2)/12
  • Hollow Sphere of radius R along its center I=2MR2/3
  • Solid Sphere of radius R along its center I=2MR2/5
• Total Kinetic Energy of Rolling Motion is K=[ mvCM2+I2 ]/2
• Total Angular Momentum of Rolling Motion is L=mvCMR+I
• Pure Rolling without slipping on stationary surface -
  • vCM=R and aCM=R
  • Forward Slipping happens when vCm>R
  • Backward Slipping happens when vCM<R
  • Total Kinetic Energy is K=(1/2)mvCM( 1+k2/R2 )
• Formulas for Pure Rolling Motion in Inclined Plane with mass M, radius R and inclination -
  • Acceleration a=gR2/( k2+R2 )
  • Minimum Frictional Coefficient =k2/(k2+R2)
• Work Done by Torque is W=d

Topic - 8: Gravitation

• Newton’s Law of Gravitation is F=Gm1m2/R2 where G6.67*10-11Nm2/kg2
• Gravitational Field is GM/R2
• Gravitational Field outside a Spherical Shell is -GM/r2 where r>R
• Gravitational Field on the Surface of the Spherical Shell is -GM/R2
• Gravitational Field inside the Spherical Shell is 0
• Gravitational Field outside a Solid Sphere is -GM/r2 where r>R
• Gravitational Field inside a Solid Sphere is -GMr/R3 where r<R
• Acceleration due to gravity is g=GM/R2
• Acceleration due to gravity at height h above the surface is gh=g(1-2h/R) when h<<<R
• Acceleration due to gravity at depth d from the surface is gd=g(1-d/R)
• Acceleration due to gravity at latitude is g=g-2R2
• Gravitational Potential due to a point mass is V= -GM/r
• Gravitational Potential inside a Spherical Shell is 0
• Gravitational Potential outside the Spherical Shell is V= -GM/r where r>R
• Gravitational Potential inside a Solid Sphere is V= -GM(3R2-r2)/2R3 where r<R
• Potential of a thin ring on the axis at a distance r is V= -GM/R2+r2
• Escape Velocity from a planet is v=2GM/R
• Orbital Velocity of a satellite is v=GM/r where r>R
• Time Period of a satellite is T=2*rr/GM
• Potential Energy of a point mass at a distance r from the center of object is U= -GMm/r
• Kinetic Energy of a satellite is K=GMm/2r
• Mechanical Energy of a satellite is E= -GMm/2r
• Kepler’s 3rd Law of Planetary Motion is T2=ka3 where a is the length of semi-major axis

Topic- 9: Solid Mechanics

• Stress is the Ratio of Internal Restoring Force per unit Area of Cross-Section
• Strain is the Ratio of change in size of the object to its original size
• Hooke's Law within elastic limit is StressStrain
• Young’s Modulus Y=( F/A )/( L/L )
• Increment in length due to its own weight L=gl2/2Y
• Bulk Modulus = -P/( V/V )
• Compressibility is the reciprocal of Bulk Modulus
• Modulus of Rigidity =(F/A)/
• Poisson’s Ratio =Lateral Strain/Longitudinal Strain= -(D/D)(L/L)
• Work Done on a wire is W=(1/2)*Stress*Strain*Volume=FL/2

Topic - 10: Fluid Mechanics

• Mass Density is =MassVolume
• Specific Weight is WeightVolume=g
• Relative Density is Density of LiquidDensity of Pure Water at 4OC
• Density of a mixture with variable Volume is =k=1nmkk=1n( mk/k )
• Density of a mixture with variable Mass is =k=1nVkkk=1nVk
• Pressure P=Normal ForceArea
• Difference of Pressure in depth h is P=hg
• Gauge Pressure at depth h of a liquid when placed in an elevator is P=h( ga )
• Gauge Pressure between two points on same level at a distance of l when the liquid is accelerated by a is P=la
• Rotating Cylinder along the length and passing through the center, th extra height is h=(r)2/2g
• Pascal’s Law: F1A1=F2A2
• Absolute Pressure=Atmospheric Pressure+Gauge Pressure
• Atmospheric Pressure is Patm=101325 N/m2
• Buoyant Force is the Weight of Displaced Fluid, FB=Vg
• Equation of Continuity is A1v1=A2v2
• Bernoulli’s Theorem is P+v2/2+gh=Constant
• Principle of Venturimeter is v=A22gh/( A12-A22 )
• Velocity of Efflux is v=2gh
• Horizontal Range of Efflux is R=2h(H-h)
• Surface Tension is Force per unit Length, T=F/l
• Surface Energy is S=TA
• Excess Pressure for water droplet is 2T/R
• Excess Pressure for soap bubble is 4T/R
• Height of Capillary Rise h=2T/rg
• Height of Capillary Rise after correction h=[ 2T/rg ]-(r/3)
• Newton’s Law of Viscosity is F=A( dv/dx )
• Stoke’s Law is F=6rv
• Poiseuille’s Formula is Q=pr4/( 8L )
• Terminal Velocity is vT=2r2(-)g/9
• Reynold’s Number is Re=vd/

Topic - 11: Thermal Physics and Thermodynamics

• Linear Expansion l=l0(1+T)
• Areal Expansion A=A0(1+T)
• Volume Expansion V=V0(1+T)
• Fractional Change in Time Period of a Simple Pendulum is T/2
• Thermal Strain l/l=T
• Thermal Stress F/A=YT
• Coefficient of Volume Expansion in Gases is =1/T
• Heat Capacity of a body is H=Q/T
• Specifc Heat Capacity is s=Q/mT
• Molar Heat Capacity is Q/nT
• Latent Heat L=Q/m
• Rate of Heat Flow is dQdt= -KAdTdx
• Thermal Resistance RT=l/KA
• Coefficient of Thermal Conduction in Series Connection is K=i=1nlii=1nli/Ki
• Coefficient of Thermal Conduction in Parallel Connection is K=i=1nKiAii=1nAi
• Stefan-Boltzmann’s Law says I=eT4 where I is the Intensity and e[0, 1]
• Prevost’s Theory of Heat Enrgy Exchange is Inet=e( T4-T04 )
• Newton’s law of Cooling is -dT/dt(T-T0) or T=T0+(Ti-T0)(-kt)
• Newton’s Law of Cooling for small temerature difference is T1-T2t=k[T1+T22-T0]
• Wien’s Displacement Law max=b/T where b2.8910-3mK
• Solar Constant S=(RST2/r)2
• Mayer’s Formula CP=Cv+R
• Average Distance between two consecutive collisions is =12d2n
• Mixture of Non-Reacting Gases -
  • Molecular Weight Mmix=k=1NnkWkk=1Nnk
  • Specific Heat Capacity at constant Volume is sV=k=1Nnk(sV)kk=1Nnk
  • Specific Heat Capacity at constant Pressure is sV=k=1Nnk(sP)kk=1Nnk
  • n-1=n11-1+n22-1+n33-1+...+nkk-1
• Molar Heat Capacity for any polytropic process is C=CV+R1-x
• First Law of Thermodynamics is Qsupplied=Wby system+U
• Work Done by the System is W=V1V2P dV
• For Adiabatic Process PV=Constant and W=(P1V1-P2V2)/(-1)
• For Isothermal Process PV=Constant and W=nRT(V2/V1)
• For Isobaric Prcess W=nRT
• Efficiency of a Carnot Cycle is =1-T1T2
• Coefficient of Performance is =T2T1-T2
• Isothrmal Bulk Modulus of Gases is = -VPV
• Adiabatic Bulk Modulus of Gases is = -VPV

Topic - 12: Oscillations and Waves

• Angular Frequency =km
• Equation for Linear SHM is d2xdt2+2x=0
• Equation for Angular SHM is d2dt2+2=0
• Displacement in SHM is x=A(t+)
• Velocity of a particle in SHM is v=A(t+)=A2-x2
• Acceleration of a particle in SHM is a= -A2(t+)= -2x
• Kinetic Energy of a particle in SHM is K=kA22(t+)/2
• Potential Energy ofa particle in SHM is U=kA22(t+)
• Total Energy of a particle in SHM is E=K+U=(1/2)kA2
• Time Period in a Spring Block System is T=2mk
• Time Period in a Combined Spring Block System is T=2k where is the reduced mass
• Time Period in a Series combination of springs is T=2mk where k is the effective Spring Constant, that is 1k=1k1+1k2+1k3+...+1kn
• Time Period in a Series combination of springs is T=2mk where k is the effective Spring Constant, that is k=k1+k2+k3+...+kn
• Time Period of a Simple Pendulum is T=2lg
• Time Period of a Physics Pendulum is T=2lg where =Moment of Inertiaml2
• Time Perod of a Conical Penduum is T=2l g
• Time Period of a Tortional Pendulum is T=2Ik
• Time Period for an SHM in a U-Tube Manometer is T=2hg where h is the height
• Time Period of a particle in SHM in a tunnel inside te Earth is T=2Rg
• Equation of a Damped Oscillation is d2xdt2+2x+bmv=0
• Displacement due to Damped Oscillation is x=A(-bt/2m)(t+)
• Angular Velocity in Damped Oscillation is =km-b24m2
• Total Energy in Damped Oscillation is E=(1/2)kA2(-bt/m)
• Equation of any wave in 2-D is 2yt2=v22yx2
• Equation of a Plane Progressive Wve in 2-D is y=A(t-kx) where k=2/
• Velocity of a wave is v=/k
• Velocity of the particle is vP=y/t=A(t-kx)
• vP= -v(dy/dx)
•  Particle Acceleration is 2y/t2= -A2(t-kx)
• Relation between Phase Difference, Path Difference and Time Difference is 2==TT
• Kinetic Energy per unit volume is (1/2)vP2=(1/2)2A22(t-kx)
• Potential Energy per unit volume is (1/2)2A22(t-kx)
• Total Energy per unit volume is 2A22(t-kx)
• Power of a wave is P=(1/2)2A2vS where S is the Area of Cross-Section
• Intensity of a wave is (1/2)2A2v
• Speed of a transverse wave on string v=T/
• Interference of two waves -
  • For amplitude A=A12+A22+2A1A2
  • For intensity I=I1+I2+2I1I2
  • For constructive Interference, =n or =2n and Imax=(I1+I2)2
  • For Destructive Interference, =(2n+1) and Imin=(I1-I2)2
  • Degree of Hearing is (Imax /Imin )-1( Imax/Imin )+1100
• Amplitude of Reflected Wave is Ar=2-12+1Ai where is the frequency
• Amplitude of Trnasmitted Wave is At=222+1Ai
• nth harmonic in stationary string wave is f=nv/2l (fixed at both ends)
• (2k-1)th harmonic in stationary wave is f=(2k-1)v/4l (fixed at one end)
• Velocity of Sound Wave with elasticity E is v=E/
• Newton’s Formula for Sound Waves v=P/
• Laplace Correction to Newton’s Fomula v=P/
• Equation of a Pressure Wave is p=ABk(t-kx)
• Frequency in a Closed End Organ Pipe is f=(2k-1)v/4l for (2k-1)th harmonic
• Error Correction in Closed End Organ Pipe is f1=v/4(l+0.6R)
• Frequency of an Open End organ Pipe is f=nv/2l for nth harmonic
• Error Correction in Open End Organ Pipe is f1=v/2(l+1.2R)
• Wavelength of a Resonating Tube is =2(l2-l1)
• End Correction in a Resonating Tube is e=(l2-3l1)/2
• Loudness of Sound (in dB) is =10(I/I0)
• Doppler’s Effect f=v+v0v-vsf

Topic - 13: Electrostatics

• Coulomb’s Law F=140q1q2r2
• Principle of Supreposition F=F1+F2+F3+...+Fn
• Electric Field E=F/q
• Electric Field due to a point charge is E=140qr2r
• Equilibrium of charges for an Equilateral Triangle is q= -q0/3
• Equilbrium of charges for a Square is = -q0(22+1)/4
• Equilbrium of two charges hanging from a point through thread T=mg and T=Fe
• Electric Potential Va= --aEdr or E= -V
• Electric Potential for a point charge is V=140qr
• Electric Potential Energy of two charges u=140q1q2r
• Electric Dipole Moment p=q2a where 2a is the total length of the dipole
• Torque on an electric dipole in a uniform electric field is =pE
• Potential Energy stored in a dipole in a uniform electric field is U= -pE
• Electric Field at Axial Point is E=1402pr3
• Electric Field at Equitorial Point is E=140-pr3
• Electric Field at any point due to an electric dipole is E=140p1+32r3
• Electric Potential at any point due to an electric dipole is V=140pr2
• Total Potential Energy due to many charges is U=Uself+ij=1n140qi qjr
• Electric Flux and Gauss’s Law =SEdA=qenclosed0
• Electric Field due to a charged spherical shell when rR is E=140Qr2
• Electric Field due to a charged spherical shell when r<R is E=0
• Electric Field due to a non-conducting sphere when rR is E=140qr2
• Electric Field due to a non-conducting sphere when r<R is E=140q rR3
• Electric Potential due to a charged spherical shell when rR is V=140Qr
• Electric Potential due to a charged spherical shell when r<R is V=140QR
• Electric Potential due to a non-conducting spherical when rR is V=140Qr
• Electric Potential due to a non-conducting spherical when r<R is V=140Q(3R2-r2)2R3
• Electric Field due to a charged ring at Axial Point is E=140q x(x2+R2)3/2
• Electric Potential due to a charged ring at Axial Point is V=140qx2+R2
• Electric Field due to a charged infinite cylinder is E=1402r where rR and is the Linear Charge Density
• Electric Field due to an infinite charged plane is E=/20 where is the Surface Charge Density
• Energy Density in Elctric Field is uE=0E2/2
• Electric Field just outside any conductor is E=/0

Topic - 14: Capacitance and Capacitors

• Capacitance C=Q/V
• Capacitance of an isolated sphere C=4R
• Capacitance of a Spherical Capacitor is C=4 ab/(b-a)
• Capacitance of a Parallel Plate Capacitor is C=A/d
• Capacitance of a Parallel Plate capacitors when Dielectric of thickness t is used is C=0Ad-(t-t/) where is the Dielectric Constant
• Capacitance of a Parallel Plate Capacitor with different dielctrics is C=0Ap=1ntp/p
• Capacitance of a cylindrical capacitor is C=2(b/a)
• Capacitance of capacitors in series is 1C=1C1+1C2+1C3+...+1Cn
• Capacitance of a capacitors in parallel is C=C1+C2+C3+...+Cn
• Energy stored in charged capacitor is U=CV2/2=QV/2=Q2/2C
• Common Potential du to sharing of charges between two capacitors is V=k=1nCkVkk=1nCk
• Force of Attraction between two capacitor plates is F=Q2/(20A)

Topic - 15: Current Electricity

• Charge I=Q/t or I=dq/dt
• Charge Density J=I/A or I=JdA or J=E
• Drift Velocity vd=E
• Drift Current Id=neAvd
• Resistivity =RA/l
• Dependence of Resistance on Temperature R=R0(1+)
• Ohm’s Law V=IR
• Kirchhoff's Current Law Iinwards=Ioutwards
• Kirchhoff’s Voltage Law Voltage=0
• Resistance in Series R=R1+R2+R3+...+Rn
• Resistance in Parallel 1R=1R1+1R2+1R3+...+1Rn
• EMF of a cell with its internal resistance is VAB=ER+r
• Cells in Series Connection I=nER+nr
• Cells in Parallel Connection I=ER+(r/m)
• Cells in Series and Parallel Connection I=mER+(mr/n)
• Principle of Wheatstone Bridge is PQ=RS
• Meter Bridge Principle S=100-llR
• Potentiometer Principle E1E2=l1l2
• Shunt Resistance for Ammeter is S=IgRgI-Ig
• Shunt Resistance for Voltmeter is S=VIg-G
• Electrical Power is P=VI=V2/R=I2R
• Joule’s Law of Heating W=VIt=I2Rt or W=0tI2R dt 
• Power for Series Combination 1P=1P1+1P2+1P3+...+1Pn
• Power for Parallel Connection P=P1+P2+P3+...+Pn

Topic - 16: Magnetic Effects of Current and Magnetism

• Biot-Savart Law dB=4I( dlr )r2 or dB=4Idlr2
• 0=410-7H/m
• For moving charge dB=4q(vr)r2
• Magnetic Field due to current carrying straight conductor is B=0I4R(1+2)
• Magnetic Field due to current carrying infinite wire is B=0 I2R
• Magnetic Field due to circular wire carrying current (at center) is B=0 I2R
• Magnetic Field due to circular wire carrying current (at axis) is B=0 IR22(x2+R2)3/2
• Magnetic Field due to circular arc at its center is B=04IR
• Magnetic Field due to infinite solid cylinder is B=042IrR2 where r<R
• Magnetic Induction due to Solenoid is B=0nI where n=N/2R
• Magnetic Field due to a current carrying sheet is B=0I/2
• Ampere’s Law LBdl=0Ienclosed
• Lorentz Force F=qE+q(vB)
• When charged particle moves undeviated then v=E/B
• Magnetic Force on a moving charge is F=q(vB) or F=q B v
• Magnetic Force due to current carrying wire is F=I(lB) or F=I B l
• Force per unit length of parallel wire carrying current is f=042I1I2d
• Torque on a magnetic dipole is =mB where m is the magnetic moment of dipole
• For a moving coil galvanometer I=k/NAB
• Force on a magnetic dipole in a non-uniform magnetic field is |F|=|mBr|
• Current produced by a rotating charge is I=q/2
• Magnetic Moment due to a rotting charge is m=qR2/2
• Magnetic Field at Axial Position of a magnetic dipole is B=042mr3
• Magnetic Field at Equatorial Point of a magnetic dipole is B=04-mr3
• Magnetic Field at any point due to a magnetic dipole is B=04m1+32r3
• Magnetic Potential due to magnetic dipole is V=04m r2
• Potential Energy of a magnetic dipole in a uniform magnetic field is U= -mB
• Magnetic Induction B=H and Magnetic Permeability =B/H
• Magnetic Susceptibility = -1
• Curie-Weiss Law says m1T-TC for Ferromagnetic materials
• F(magnetic)F(electric)=v2c2

Topic - 17: Electromagnetic Induction

• Magnetic Flux =BA for uniform Magnetic Field
• Magnetic Flux =BdA for variable Magnetic Field
• Faraday’s Law of Electromagnetic Induction EMFd/dt
• Lenz's Law of Electromagnetic Induction EMF= -d/dt
• EMF induced in a straight conductor in uniform Magnetic Field is EMF=Blv
• EMF induced in a rotating rod is EMF=BL2/2
• Self Inductance L=/I
• Self induced EMF is EMF= -L*dI/dt
• Series combination of inductors L=L1+L2+L3+...+Ln
• Parallel combination of inductors 1/L=1/L1+1/L2+1/L3+...+1/Ln
• For Transformers EMFVoltage
• Efficiency of a Transformer is =Output PowerInput Power
• Magnetic Field due to Solenoid is B=nI
• Self Inductance of a Solenoid is L=0n2AL
• Growth of Current in L-R Circuit I=( EMFR )[ 1-( -Rt/L ) ]
• Current Decay I=I0( -Rt/L )

Topic - 18: Alternating Current and EM Waves

• Iavg=0TI dt0T dt
• IRMS=0TI2 dt0T dt
• If V=V0(t) then Vavg=2V0/ and VRMS=V0/2
• If I=I0(t) then Iavg=2I0/ and IRMS=I0/2
• Impedance of an LCR Circuit is Z=R2+( XL-XC )2
• Power Factor==R/Z
• Energy in an LC Circuit is E=LI2/2
• For Series LCR Circuit d2dt2+RLdqdt+qLC=V0L(t)
• For Parallel LCR Circuit d2dt2+1RCddt+LC=V02C(t)
• Poynting Vector S=(1/0)( EB )
• Maxwell correction for Ampere’s Law is Bdl=0[ Ic+0( d/dt ) ]

Topic - 19: Ray Optics and Wave Optics

• Reflection in Vector Form is r=e-2(en)n
• Number of images in inclined mirror is 3600/n
• Mirror Formula 1f=1u+1v
• Transverse Magnification m=h2/h1= -v/u
• Optical Power P=1/f
• Law of Refraction in Vector Form is (en)r=0
• Snell’s Law 21=ir
• Lateral Shift is x=t(i-r)r
• Apparent Shift is x=t(1-1/)
• Critical Angle in Total Internal Reflection is iC=-1(r/i)
• Angle of Deviation in Prism is =(i1+i2)-(r1+r2) and A=r1+r2
• When =min then i1=i2 and r1=r2, therefore glass=[ (A+min)/2 ](A/2)
• For small angles Prism, v-ry=v-r-1 where =(v+r)/2
• For the Refraction at Spherical Surface 2v-1u=2-1R
• Lens Makers Formula 1f=(-1)[1R1-1R2]
• Lens Formula 1f=1v-1u
• Magnification of Lens is m=v/u
• Power of a Lens is P=1/f
• For the combination of Lens placed in contact to each other 1f=1f1+1f2
• Newton’s Formula for Lens f=Distance of Object from Focus*Distance of Image from Focus

Topic - 20: Modern Physics

• Energy of a Photon is E=h
• Linear Momentum of a Photon is p=h/
• Intensity of Light is I=P/A
• Pressure on perfectly reflecting surface is P=2I/c
• Pressure on perfectly absorbing surface is P=I/c
• Einstein’s Photoelectric Equation is h=K+W0
• Stopping Potential V=Kmax/e
• De Broglie wavelength =h/mv
• Kinetic Energy if a particle is K=p2/2m
• Momentum of a particle is 2mK
• For Bohr Atomic Model, mvr=nh/2
• Radius of nth Circular Orbit is r=[ 0.529 n2/Z2 ] A
•  Energy of an electron in nth orbit is E= (-13.6 Z2/n2 )eV and Binding Energy is B= -E
• The formula for Wave Number is =R[ n1-2-n2-2 ] where R is the Rydberg’s constant
• For X-Rays min[ 12400/V ]A
• Moseley's Law for Characteristic Spectrum =a(Z-b)
• Bragg’s Law for Diffraction n=2d
• Mass Defect in nuclear Fusion is m=[ Mass of Reactants-Mass of Products ]
• Law of Radioactive Decay N=N0(-kt) where k is the Decay Constant
• Half-Life of a Radioactive material t=2/k
• Number of Nuclei left after n Half-Life is N=N0/2n
• Mass-Energy Equivalence E=mc2
• Radius of a Nucleus is R3=( 1.3*10-15 )3*A
• Radioactive Disintegration with Succession N=(/k)( 1-(-kt) )

Topic - 21: Semiconductors and Communication System

• Number of Electrons reaching from Valence Band to Conduction Band is n=AT3/2exp(- E/2kT )
• Mass-Action Law is n2=ne*nh
• Conductivity =ne( e+h )
• Form Factor f=IRMSIDC
• Form Factor for Half Wave Rectifier is /2
• Form Factor for Full Wave Rectifier is /22
• Ripple Factor is r=IACIDC
• Ripple Factor for Half Wave Rectifier is r1.21
• Ripple Factor for Half Wave Rectifier is r0.48
• Rectifier Efficiency is n=PDCPAC

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