JEE Advanced 2024: One Month to Go for Exam, Check Important Physics Formulas

Kinematics Formulas

• Average speed = Total distance/Total time
• Average velocity = Total displacement/Total time
• Acceleration = (Final velocity - Initial velocity) / Time taken
• Final velocity = (Initial velocity + Acceleration) × Time taken
• Displacement = (Initial velocity + Final velocity) / 2 × Time taken

Newton's Laws of Motion

• F = m × a  (Newton's Second Law of Motion)
• Force of friction = μ × N  (where μ  is the coefficient of friction and N is the normal force)
• Weight =m × g  (where g is the acceleration due to gravity)
• Impulse = force × time
• Law of Conservation of Momentum: Momentum before collision = Momentum after collision

Work, Energy, and Power Formulas

• Work = force × displacement × cosθ
• Kinetic Energy = 0.5 × m × v²
• Potential Energy = m × g × h
• Total Mechanical Energy = Kinetic Energy + Potential Energy
• Power = work done/time taken

Electric Charge and Fields Formulas

• Electric Field = force per unit charge = F/Q
• Coulomb's Law: F = {k×(q₁×q₂)} / r²
• Electric Potential Energy = q×V
• Electric Potential = V/d

Energy of electric dipole

U = –ρE

Energy of a magnetic dipole

U = –μBC

Electric Charge

Q = ±ne

(where e = 1.60218 ×10⁻²⁹ C), SI unit of Electric Charge is Coulomb

Coulomb’s Law

Electrostatic Force (F) = k[q₁q₂/r²]

and,

In Vector Form:

→F = k(q₁q₂) × →r/r³,

Where,

• q₁ and q₂ are Charges on the Particle
• r = Separation between them,
• →r = Position Vector
• k = Constant = 14πϵ₀ = 8.98755 × 109Nm²C²

Electric Current

The current at Time t: i = limΔt→0 ΔQ/Δt = dQ/dT

Where ΔQ and ΔT = Charges cross an Area in time ΔT. SI unit of Current is Ampere (A) and 1A = 1 C/s

Average current density

• →j = Δi/Δs
• J = limΔs→0 Δi/Δs=di/dS
• J = Δi/ΔS cos θ

Where,

ΔS = Small Area,

Δi = Current through the Area ΔS,

P = Perpendicular to the flow of Charges,

Θ = Angle Between the normal to the Area and the direction of the current.

Kirchhoff’s Law

Law of Conservation of Charge: I₃ = I₁+I₂

Resistance

• Resistivity: ρ(T) = ρ(T0)[1+α(T−T0)]
• R(T)=R(T0)[1+α(T−T0)]

Where,

ρ(T) and ρ(T0) are Resistivity at Temperature T and T0 respectively,

α = Constant for a given material.

Lorentz Force

→F = q[→E +(→v × →B )]

Where,

E = Electric Field,

B = Magnetic Field,

q = Charge of Particle,

v = Velocity of Particle.

Magnetic Flux

Magnetic Flux through Area dS = φ= →B⋅→dS = B⋅dS cosθ

Where,

→dS  = Perpendicular vector to the surface and has a magnitude equal to dS,

→B = Magnetic Field at an element,

Θ = Angle Between →B and →dS,

SI unit of Magnetic Flux is Weber (Wb).

Straight line Equation of Motion (Constant Acceleration)

• v = u + at
• s = ut + 1/2at²
• 2as = v² − u²

Gravitational Acceleration Equation of Motion

Motion in Upward Direction

• v = u − gt
• y= ut − 1/2gt²
• −2gy = v² − u²

Motion in Downward Direction

• v = u + gt
• y= ut + 1/2gt²
• 2gy = v² − u²

Projectile Equation of Motion

• Horizontal Range (R) = u²sin2θ/g
• Time of Flight (T) = 2usinθ/g
• Maximum Height (H) = u²sin2θ/2

Where,

u = initial velocity,

v = final velocity,

a = constant acceleration,

t = time,

x = position of particle.

Laws of Gravity

Gravitational force →F = G[Mm/r²]r

Where,

M and m = Mass of two Objects,

r = separation between the objects,

∩r = unit vector joining two objects,

G = Universal Gravitational Constant, [G = 6.67 × 10−11Nm²Kg⁻²]

Work Done by Constant Force

Work Done W = →F⋅→S = |→F||→S|cosθ,

Where, S = Displacement along a straight line,

F = applied force,

Θ = Angle between S & F.

It is a scalar quantity and the Dimension of work is [M¹L²T⁻²]. SI unit of Work is the joule (J) and 1J = 1N⋅m = Kgm²s⁻²

Kinetic Friction

Fk = μk⋅N

Maximum Static Friction (Limiting Friction): f_max = μs⋅N,

Where, N = Normal Force,

μk = Coefficient of Kinetic Friction,

µs = Coefficient of Static Friction.

Simple Harmonic Motion

Force (F) = –kx and k = ω²m

Where,

k = Force Constant,

m = Mass of the Particle,

x = Displacement

ω² = Positive Constant.

Torque

M = r×F

Where,

r is the vector from the point P to any point A on the line of action L of F.