Class 12 Physics Electromagnetic induction Notes

Class 12 Physics Electromagnetic induction Notes
Chapter 18 – Electromagnetic Induction | Nepal eNotes
PHYSICS • CHAPTER 18

Electromagnetic Induction

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Electromagnetic Induction

Magnetic flux (φ)

The total number of magnetic lines of force passing normally through a surface is called magnetic flux.

φ = B⃗ · A⃗
φ = BA cosθ
Its unit is Weber (Wb).

Faraday’s law of electromagnetic induction

  1. Whenever flux linked with coil changes an emf is induced.
  2. The induced emf is directly proportional to rate of change of flux.
E ∝ dφ/dt
E = −dφ/dt

Electromagnetic induction

The process in which an electric current is induced due to change in magnetic flux is called electromagnetic induction.

Lenz’s law

It states that the direction of induced emf is such that it opposes the change in flux.

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Lenz’s law and conservation of energy

Mechanical energy to move the magnet towards the coil is converted into electrical energy. The induced electrical energy is converted into magnetic energy and the magnetic energy due to induced current again converted into mechanical energy to repel the magnet.

This shows energy is converted from one form to another form, so Lenz’s law follows principle of conservation of energy.

Fleming’s right hand rule

Used to find the direction of induced current during electromagnetic induction. If we stretch three fingers: the thumb, forefinger and center finger of right hand mutually perpendicular to each other such that the forefinger points the direction of magnetic field, thumb points the direction of motion of conductor, then the center finger points the direction of induced current in the conductor.

Thumb: motion Forefinger: B Center finger: I

Emf induced in a conductor (moving in uniform magnetic field)

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Q.N: Does Lenz’s law follow principle of conservation of energy?

The mechanical energy applied by a system is converted into K.E. of magnet and electrical energy in the coil. Hence Lenz’s law follows principle of conservation of energy.

Motional emf

The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf.

Consider a conductor of length l moving in a magnetic field B with velocity v. When the conductor moves magnetic flux linked with the conductor changes.

Suppose in small time dt the conductor moves through small distance dx.

Area swept by conductor (A) = lx
Flux linked with area (φ) = BA cosθ
= BA
= Blx
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According to Faraday’s law:

E = −dφ/dt
= −d(Blx)/dt
= −Bl(dx/dt)
E = −Blv = Blv

Also, induced current:

I = E/R = Blv/R

And force on conductor:

F = IlB sinθ
= (Blv/R) × lB sin90°
F = B²l²v/R

Induced emf in a rectangular coil in uniform magnetic field

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Consider a rectangular coil having N turns area A is rotating with velocity ω in a uniform magnetic field B.

Flux passing through coil is:

φ = B⃗ · A⃗
= BA cosθ
= BA cosωt

Then induced emf is given by:

E = −N dφ/dt
= −N d/dt (BA cosωt)
= −NBA d/dt(cosωt)
= −NBA(−sinωt)ω
E = NBAω sinωt
If E = Emax sinωt, then Emax = NBAω.

A.C. generator

Principle

It is based on the principle of electromagnetic induction i.e. whenever magnetic flux changes in the coil an emf is induced.

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Construction

A.C. generator has following parts:

Armature

It is a rectangular coil of insulated copper wire having N turns.

Permanent magnet

Two poles magnet produce strong magnetic field.

Slip rings

Slip rings R1 and R2 are connected to ends of armature.

Brushes

Two metallic brushes used to connect slip rings and the output.

Working

When coil rotates, the magnetic flux linked with coil changes and an emf is induced.

N S rotation R₁ R₂ brush brush
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Flux linked with coil is:

φ = B⃗ · A⃗
= BA cosωt

The induced emf is given by:

E = −N dφ/dt
= −N d/dt(BA cosωt)
= −NBA d(cosωt)/dt
E = NBAω sinωt

This expression for induced emf in AC generator.

When NBAω = E0
E = E0 sinωt
and induced current:
I = I0 sinωt

Self induction

The process in which an emf is induced in a coil by passing changing current through it.

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The property of coil due to which it opposes the change in current passing through it is called self-inductance (L).

φ ∝ I
φ = LI
L = φ/I

[I = induced current]

Also, induced emf:

E = −dφ/dt
E = −d(LI)/dt
E = −L dI/dt

Self inductance of solenoid

Consider a solenoid having n turns per unit length and carrying current I. The magnetic field due to solenoid is:

B = μ0nI
= μ0NI/l

Then magnetic flux linked to solenoid:

φ = NBA = (μ0N²IA)/l
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LI = μ0N²IA/l
L = μ0N²A/l

Mutual induction

It is the process in which an emf is induced in one coil due to change in current in another coil.

Energy stored in inductor

Suppose an inductor having N turns and carrying current I.

The emf induced is:

E = −L dI/dt

The power supplied to pass current is:

P = E × I
dW/dt = (L dI/dt)I
dW = LI dI

So, the total work done to pass current from 0 to I:

W = ∫0I dW
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W = ∫0I LI dI
W = LI²/2

Then, energy stored in inductor is:

U = 1/2 LI²

Transformer

It is an electrical device that can increase or decrease the voltage.

  • Step-up → increase voltage.
  • Step-down → decrease voltage.

Principle

Transformer works on the principle of mutual induction.

Working

Primary Secondary soft iron core
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A transformer has a soft iron core having many insulated strips in which coil is wound. Let primary coil has Np turns and Ep similarly secondary coil has Ns turns and Es emf.

Ep = −Np dφ/dt    …(1)
Es = −Ns dφ/dt    …(2)

Dividing equation (1) by equation (2):

Ep/Es = Np/Ns
Ep/Es = Np/Ns
Case (i): If Ns > Np, Es > Ep → step-up transformer.
Case (ii): If Np > Ns, Ep > Es → step-down transformer.

Note: Ideal transformer = a transformer having 100% efficiency is ideal transformer and:

output power = input power

Factors for energy loss in transformer

1. Copper loss

  • Loss due to heating of coil.
  • Can be minimized by using thick coils.
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2. Eddy current loss

  • Loss due to eddy current in the metallic plate (core) in the form of heat.
  • Minimized by using slotted and insulated core.

3. Flux loss

  • Loss due to leakage of flux.
  • Minimized by using soft iron core.

4. Hysteresis loss

  • Loss due to magnetization and demagnetization of core.
  • Minimized by using soft iron core.

5. Humming loss

  • Loss due to magnetization and demagnetization of core in the form of sound.
  • Minimized by using ferromagnetic substance.

Eddy current

The current produced in the metallic plate when it is kept in magnetic field is called eddy current.

Energy is lost due to eddy current in the form of heat.

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