JEE Exam » JEE Important Formulas » JEE Physics Important Formulas Part -4

JEE Physics Important Formulas Part -4

In this article we will go through physics quick formula revision for JEE 2022. Find the important formulas of Electromagnetic Induction, Electromagnetic waves, Electrostatics and Friction.

Electromagnetic Induction Formula

The formula for electromagnetic induction are as stated below

DescriptionFormula
Magnetic Flux

The magnetic flux through a plane of area dA placed in a uniform magnetic field B is given as

ϕ=∫ B ⃗∙dA ⃗

When the surface is closed, then magnetic flux will be zero. This is due to magnetic lines of force are closed lines and free magnetic poles is not exist

Electromagnetic Induction: Faraday’s Law

First Law: Whenever magnetic flux linked with a circuit changes with time, an induced emf is generated in the circuit that lasts as long as the change in magnetic flux continues.

Second Law: According to this law, the induced emf is equal to the negative rate of change of flux through the circuit.

E = –dϕdt

Lenz’s Law

The direction of induced emf or current in the circuit is in such a way that it opposes the cause due to which it is produced. Therefore,

E = -dϕ/dt
Induced emf   

Induced emf is given as

E = -N(dϕ/dt)E = -N((ϕ_1- ϕ_2)/t)
Induced Current   I=E/R = N/R(dϕ/dt)= N/R((ϕ_1- ϕ_2)/t)
Self – Induction

Change in the strength of flow of current is opposed by a characteristic of a coil is known as self-inductance. 

It is given as ϕ=LI

Here, L = coefficient of self – inductance

Magnetic flux rate of change in the coil is given as 

Idϕ/dt = L dl/dt=-E
Mutual – Induction

Mutual – Induction is given as 

e_2=(d(N_2 ϕ_2)/dt = M (dl_1)/dt

Therefore,

M=(μ_0 N_1 N_2 A)/l

Electromagnetic waves

The formula for electromagnetic waves are as stated below

DescriptionFormula
Gauss’s law for electricity∮ E⋅dA=Q/ε_0

Here, E is the electric field, A is the area, Q is the charge and  ε_0 is the permittivity of free space.

Gauss’s law for magnetism∮ B⋅dA=0B is the magnetic field and A is the area.
Faraday’s law∮ E⋅dl=-(dΦ_B)/dt

Here, E is the electric field, l is the length of the conductor, Φ_B  is the magnetic flux and t is the time.

Ampere- Maxwell law

∮ B⋅dl=μ_0 i+μ_0 ε_0 (dΦ_B)/dt 

Here, B is the magnetic field, l is the length of the conductor, μ_0
 is permeability of free space, i is the current flowing through the conductor, ε_0 is the permittivity of free space,Φ_B is the magnetic flux and t is the time.

Speed of light in vacuum c=1/√(μ_0 ε_0 ) 

Electrostatics formula

The formula for electrostatistics are as stated below

DescriptionFormula
Electrostatic force between two-point charges

 

F=1/4Π∈ q1q2/r2 r

Here, ε_0
 is the permittivity of free space, q1 q2 are the point charges and r is the distance between the charges.

Electric fieldE ⃗=F ⃗/q_0

Here, F is the electrostatic force experienced by test charge q0.

Electric field due to a uniformly charged ringE_axis=KQx/(R^2+x^2 )^(3/2)

Here, K is the relative permeability, Q is the charge on the ring, x is the perpendicular distance from the ring to the point at which the electric field is to be calculated and R is the radius of the ring.

Electric field due to a uniformly charged discE=σ/(2ε_0 ) [1-x/√(R^2+x^2 )]

Here, σ is the surface charge density, ε_0is the permittivity of free space, x is the perpendicular distance from the centre of the disk and R is the radius of the disk.

Work done by external force

The work done by an external force in bringing a charge q from potential V_Bto V_A is:

W=q(V_A-V_B )̂
Electrostatic potential energyU=qV
Here, q is the charge and V is the potential.
Electrostatic energy

U=1/(4πε_0 ) (q_1 q_2)/r

here q1q2 are the charges and r is the distance between the charges.

Electric potential at a point due to a point chargeV=1/(4πε_0 ) q/r
Dipole moment

The formula for calculating electric dipole moment is

p ⃗=qd ⃗

Here q is the magnitude of the charge and d is the distance between the charges.

Potential at a point due to dipole

The potential at a point due to a dipole is given as:

V=1/(4πε_0 ) (p cos θ )/r^2

Here, p is the dipole moment and θ is the angle made by the line joining the point and the centre of the dipole with the line joining the charges and r is the distance from the point at which the potential is to be calculated and the line joining the charges.

Torque experienced by dipole due to electric field τ ⃗=p ⃗×E ⃗ here, p is the dipole moment and E is the electric field.

Friction formula

The formula for friction are as stated below

DescriptionFormula
Force due to kinetic friction

The formula for calculating the force due to kinetic friction is:

F_k=μ_k R

here, F_k is the force due to kinetic friction, μ_k  is the coefficient of kinetic friction and R is the normal reaction force on the body on which the force is acting.

If the body is lying on levelled plane, then the normal force is given as:

R=mg

Here m is the mass and g is the gravitational acceleration.

When the body is lying on a plane that is at some angle with the horizontal then the normal reaction force on the body is given as:

R=mgcosθ

Force due to static friction

The formula for calculating the force due to static friction is:

F_s=μ_s R

here, Fs is the force due to static friction, μ_s is the coefficient of static friction and R is the normal reaction force on the body.

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