Electro Maganetic Induction: Faraday's Laws, Lenz Laws and BH Characteristics,Emf

The induction of an electromotive force by the motion of a conductor across a magnetic field or by a change in magnetic flux in a magnetic field is called ‘Electromagnetic Induction’. The emf is known as induced emf and the current driven by it is known as induced current.

This either happens when a conductor is set in a moving magnetic field (when utilizing AC power source) or when a conductor is always moving in a stationary magnetic field.

Faraday’s law of Electromagnetic Induction

• First law:  Whenever a conductor is placed in a varying magnetic field, EMF induces and this emf is called an induced emf and if the conductor is a closed circuit than the induced current flows through it.
• Second law: The magnitude of the induced EMF is equal to the rate of change of flux linkages.

Based on his experiments we now have Faraday’s law of electromagnetic induction according to which the amount of voltage induced in a coil is proportional to the number of turns and the changing magnetic field of the coil. So now, the induced voltage is as follows:

e = N × dΦ/dt

where,
e is the induced voltage,
N is the number of turns in the coil,
Φ is the magnetic flux,
t is the time.

Lenz’s law of Electromagnetic Induction

Lenz law of electromagnetic induction states that, when an emf induces according to Faraday’s law, the polarity (direction) of that induced emf is such that it opposes the cause of its production.

According to Lenz’s law

E = -N (dΦ/ dt)   (volts)

Magnetic Leakage or Leakage Flux: - 

 

As the current through the primary winding produces flux. The flux ϕm which links both the windings is the useful flux and is known as mutual flux. Although, a part of the flux (ϕ1) produced by the primary current does not link with the secondary winding. When load is connected across the secondary winding, a current flow through it and produces a flux (ϕ2), which links only with the secondary winding. Thus, the fluxes such as ϕ1 or ϕ2 which links only one winding is known as leakage flux. 

The leakage flux paths are mainly through the air which has very high reluctance. Therefore, the effect of primary leakage flux (ϕ1) is to introduce an inductive reactance (X1) in series with the primary winding. Similarly, the secondary leakage flux (ϕ) introduces an inductive reactance (X2) in series with the secondary winding. 

 

However, the leakage flux in a practical transformer is very small (about 5% of ϕm), yet it cannot be ignored. Because, the leakage flux paths are through the air, which has very high reluctance. As a result, it requires considerable emf. 

EMF Equation of a Transformer: - 

 

 

 

Now rate of change of flux per turn means induced EMF in volts. 

Average EMF / per turn = 4f Φm volt. 

If flux Φm varies sinusoidally, then RMS value of induced EMF  is obtained by multiplying the average value with form factor. 

Form factor= RMS value / Average value = 1.11 

RMS value of EMF / turn = 1.11. 4f Φm= 4.44f Φm volt 

Now RMS value of the induced EMF in the whole primary winding. 

= ( induced EMF / turn) x number of primary turns 

E1 = 4.44 x f x N1 Φm ……….. (i) 
 

E1 = 4.44 xf N1 Bm A … [as  (Φm = BmA)] 

Similarly, RMS value of the EMF induced in secondary is E2 = 4.44 x f N2 Φm ……….. (ii) 
 

E2 = 4.44 x f N2 Bm A.  … [as  (Φm= BmA)] 

It’s seen from (i) and (ii) that: EMF Equation of the Transformer = 
 

E1 / N1= E2 / N2 = 4.44 x f Φm.  …… (iii) 

It means that EMF / turn is the same in both the primary and secondary windings in the transformer i.e. flux in Primary and Secondary Winding of the Transformer is same. 
 

Moreover, we already know that from the power equation of the transformer, i.e, in ideal Transformer (there are no losses in transformer) on no-load, 

V1 = E1 

and 

E2 = V2 

Where, 

V1 = supply voltage of primary winding 

E2 = terminal voltage induced in the secondary winding of the transformer. 

Voltage Transformation Ratio (K) 

As we have derived from the above EMF equation of the transformer (iii); 

E1 / N1= E2 / N2 = K 
 

Where, 

K = Constant 

The constant “K” is known as voltage transformation ratio. 

If N2 > N1, i.e. K > 1, then the transformer is known as a step-up transformer. 

If N2 < N1, i.e. K < 1, then the transformer is called step-down transformer. 

Where, 

N1 = Primary number of turns of the coil in a transformer. 

N2 = Secondary number of turns. 

Applications of Electromagnetic Induction

1. Electromagnetic induction in AC generator
2. Electrical Transformers
3. Magnetic Flow Meter

Statically induced E.M.F

Here the conductor/ coil and magnetic field system both are stationary.

Self Induction

We know that a current-carrying coil produces a magnetic field and there is a flux of this magnetic field through the coil itself. where there is a change in  the current through the coil. there will be a change in the magnetic flux through the coil and hence according to faradays law, an emf will be induced. This phenomenon to which an emf is induced in a current-carrying coil due to a change in its own current is known as self-induction. Its given as 

e=−Ldidt

where L is inductance. it depends on the shape and size of the coil. SI unit of inductance is henry. any conducting loop which can exhibit self-induction is called an inductor.

Coefficient of Self inductance L = Nϕ/I  henry.

Where

N = Number of turns in the coil.

ϕ = flux linking with the coil.

I = Current flowing through the coil.

Nϕ= Flux linkages.

Mutual Induction

When a current carrying coil is placed near another conducting coil, there is a magnetic flux through the second coil due to the magnetic field of the first coil. Now, if there is a change in the current in the first coil. there will be a change in the magnetic flux associated with the second coil and hence according to faraday's laws, an emf will be induced in the second coil. This phenomenon due to which an emf is induced in the second coil is known as Mutual Induction.

 

where 

 N_m = number of turns in coil 2.

BH Characteristics

A magnetic material is identified and characterized by its B-H characteristics. In free space or in air the relationship between the two is linear and the constant of proportionality is the permeability μ0. If B is plotted against H, it will be a straight line. However, for most of the materials the relationship is not linear.

H and B are given by-

H=Nl/I(current)

B=φ/a

where,

N = number of turns

l (in m) = mean length of the flux path

a (in ㎡) = cross-sectional area

I (in A) = reading of the ammeter

φ (in Wb or Weber) = reading of the flux meter

BH Curve

The curve shows the relationship between the magnetization force and magnetic flux density of a magnetic substance is known as the BH curve, where B - the flux density i.e,φ/a  and H - the magnetizing force i.e, Nl/I.

Lets the coil has N turns and l length. so H ∝ I and the current showing by ammeter indicate the magnetizing force.

Uses of BH Curve

1. It is used to find out the saturation point of the magnetic materials, so it is useful for designing purpose.
2.it is used to find out the permeability i.e, B/H of the material.