JEE Physics Important Formulas Part -4

Electromagnetic Induction Formula

The formula for electromagnetic induction are as stated below

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

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

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

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,

Induced emf is given as

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 

Mutual – Induction is given as 

Therefore,

Electromagnetic waves

The formula for electromagnetic waves are as stated below

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

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

∮ 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.

Electrostatics formula

The formula for electrostatistics are as stated below

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.

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

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.

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.

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

U=1/(4πε_0 ) (q_1 q_2)/r

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

The formula for calculating electric dipole moment is

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

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

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.

Friction formula

The formula for friction are as stated below

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

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.