Overview - Electromagnetic Induction

• Moving electric charges produce magnetic fields, showing that electricity and magnetism are related.
• A changing magnetic field can produce an electric current in a closed coil.
• This process is called electromagnetic induction.
• Electromagnetic induction is the working principle of generators and transformers.

Magnetic flux is the dot product of magnetic field and area vector.

Φ_B​ = B ⋅ A = B A cos θ

Φ_B ​= ∑B_i ​⋅ dA_i

or

​Φ_B​ = ∫B ⋅ dA

The emf induced in a conductor due to its motion in a magnetic field is called Motional Electromotive Force (Motional EMF).

ε = Blv

Where:

• B = magnetic field
• l = length of conductor
• v = velocity of conductor

F = q(E + v × B)

For stationary conductor (v = 0):

F = qE

The constant of proportionality between flux linkage and current is called Inductance.

That is, NΦ_B​ ∝ I

• It is a scalar quantity'
• Dimensions = [M L² T^–2 A^–2]

The constant of proportionality between the flux linkage of one coil and the current in another coil is called Mutual Inductance.

N_1​Φ_1​ = M₁₂​I₂

​N₂​Φ₂​ = M₂₁​I₁

Two Long Co-axial Solenoids:

M = μ₀​n₁​n₂​πr₁²​l

• Current in one coil produces a magnetic flux that links a nearby coil.
• Mutual inductance depends on the number of turns, size, length, separation, and orientation of the coils.
• For long co-axial solenoids, the magnetic field inside is considered uniform and edge effects are neglected.
• The mutual inductance between two coils is the same in both directions.
• A changing current in one coil induces emf in the other coil, and the induced emf increases with faster change of current.

The phenomenon in which an emf is induced in a coil due to a change of current in the same coil is called Self-Induction.

OR

The constant of proportionality between flux linkage and current in the same coil is called Self-Inductance (L).

Self-Inductance Relation:

NΦ_B ​= LI

Self-Induced EMF:

\[\varepsilon=-L\frac{dI}{dt}\]

Self-Inductance of a Long Solenoid:

L = μ₀​n²Al

W = \[\frac {1}{2}\]LI²

A device that converts mechanical energy into electrical energy using the principle of electromagnetic induction.