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 asϕ=∫ 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
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 is given asE = -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 asIdϕ/dt = L dl/dt=-E
|Mutual – Induction|
Mutual – Induction is given ase_2=(d(N_2 ϕ_2)/dt = M (dl_1)/dt
Therefore,M=(μ_0 N_1 N_2 A)/l
The formula for electromagnetic waves are as stated below
|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
|Speed of light in vacuum||c=1/√(μ_0 ε_0 )|
The formula for electrostatistics are as stated below
|Electrostatic force between two-point charges|
F=1/4Π∈ q1q2/r2 r
|Electric field||E ⃗=F ⃗/q_0|
Here, F is the electrostatic force experienced by test charge q0.
|Electric field due to a uniformly charged ring||E_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 disc||E=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 energy||U=qV |
Here, q is the charge and V is the potential.
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 charge||V=1/(4πε_0 ) q/r|
The formula for calculating electric dipole moment isp ⃗=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.|
The formula for friction are as stated below
|Force due to kinetic friction|
The formula for calculating the force due to kinetic friction is:
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:
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:
|Force due to static friction|
The formula for calculating the force due to static friction is:
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.
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.