Revision Notes: Electromagnetic Induction | Physics for JEE Main & Advanced PDF Download

Magnetic flux

andϕ_B = µnAH

Here, µ is the permeability of the medium, n is the number of turns, A is the area and H is the magnetic field intensity.

(a) When θ = 90º, cosθ = 0. So, ϕ_B = 0
This signifies, no magnetic flux is linked with surface when the field is parallel to the surface.

(b) When θ = 0º, cosθ = 1. So,(ϕ_B)_max = 1
This signifies, magnetic flux linked with a surface is maximum when area is held perpendicular to the direction of field.

Faraday’s law of electromagnetic induction

(a) Whenever magnetic flux linked with a circuit changes, an e.m.f is induced in it.

(b) The induced e.m.f exists in the circuit so long as the change in magntic flux linked with it continues.

(c) The induced e.m.f is directly proportional to the negative rate of change of magnetic flux linked with the circuit.

So, E = -dϕ_B/dt

Negative sign is due to the direction of induced e.m.f.

Induced electric field

Lenz’s Law

It states that direction of induced e.m.f. is such that it tends to oppose the very csause which produces it. The induced e.m.f. always tends to oppose the cause of its production.

Motion of a straight conductor in a uniform magnetic field:-
(a) W = Bevl
(b) Motional e.m.f, E = Bvl
(c) Induced current, I = E/R = Blv/R
(d) F = IlB = B²l²v/R
(e) P = Fv = IlBv = B²l²v²/R
(f) H = I²R = B²l²v²/R                             

Motion of a loop in a magnetic field when whole of the coil is in the magnetic field:

(a) Motional e.m.f , E = 0
(b) Resultant Current, I = 0
(c) Force, F = 0
(d) Power, P = 0

Motion of a loop in a magnetic field when a part of the loop is out of the magnetic field:-

(a) ϕ_B = Blx

(b) Induced e.m.f , E = Blv

Power in Various Scenarios

Power

• P = I²R = E²/R
• P = B²l²v²/R       (Since, E = Blv)

(a) Coil out of field:- ϕ_B =0, E = 0, P = 0
(b) Coil entering the magnetic field:-
ϕ_B increases gradually
E = a negative constant
P = a positive constant

(c) Coil moving in the magnetic field:-
ϕ_B = Constant
E = 0
P = 0

(d) Coil leaving the magnetic field:-
ϕ_B decreases gradually
E = a positive constant
P = a positive constant
(e) Coil out of magnetic field:-
ϕ_B = 0
E = 0
P = 0

Self-Induction

(a) Magnetic flux, ϕ_B = LI
Here L is the coefficient of self -induction.
(b) e.m.f., E = -L [dI/dt]
(c) L = µ₀ µ_rnNA
Here, n is the number of turns per unit length

Series and parallel combination
(a) L = L₁+L₂ (If inductors are kept far apart and joined in series)
(b) L = L₁+L₂±2M   (If inductors are connected in series and they have mutual inductance M)
(c) 1/L = 1/L₁ + 1/L₂ (If two conductors are connected in parallel and are kept for apart)
(d) M = K√L₁L₂      (If two coils of self-inductances, L₁ and L₂ are over each other)

Inductance of Different Configurations

Inductance of wire

• L = µ₀l/8π

Inductance of hollow cylinder

• L = µ₀l/2π [ln 2l/a -1],  l >> a

Inductance of parallel wires

• L = µ₀l/π [ln d/a -1], l >> d, d >> a

Inductance of Coaxial conductor

• L = µ0l/π [ ln b/a]

Inductance of Circular loop

• L = µ0l/2π [ln 4l/d – 2.45]
• l = -2πρ0, ρ0 >> d

Inductance of Solenoid:

• L = µ₀N²S/l
• L >> a

Inductance of Torus (of circular cross section):-

L = µ₀N² [ρ₀ - √ ρ₀² – a²]

Inductance of Sheet:-

L = µ₀2l [ln (2l/b+t) + 0.5] 

Energy Stored in a Conductor

(b) U_B = B²/2µ₀

Mutual Induction
Mutual induction of two circuits is the phenomenon where a current changing in the first coil results in the induction of an e.m.f. in the second.

Coefficient of Mutual Induction
ϕ_B = MI and E = -M[dI/dt]
Here M is called the coefficient of mutual induction of two circuits.
The value of M, M =  µ₀ µ_rn₁ N₂ A
M depends upon,
(a) Area of cross-section of the two coils
(b) Number of turn of each coil
(c) Distance between the two coils
(d) Nature of material used as core

Fleming’s Right Hand Rule

Coil Rotating in a Uniform Magnetic Field

Growth and Decay of Current in LR Circuit

(a) I = I₀(1-e^-t/τ) (for growth), Here τ = L/R
(b) I = I₀e^-t/τ (for decay), Here τ = L/R