Faraday's Laws of Electromagnetic Induction

Faraday's Laws of Electromagnetic Induction

AU : May-19

• From the experiment discussed above, Michael Faraday a British scientist stated two laws of electromagnetic induction.

1. First Law

Whenever the number of magnetic lines of force (flux) linking with a coil or circuit changes, an e.m.f. gets induced in that coil or circuit.

2. Second Law

 • The magnitude of the induced e.m.f. is directly proportional to the rate of change of flux linkages (Flux × Turns of coil).

Flux linkages = Flux × Number of turns of coil

The law can be explained as below.

Consider a coil having N turns. The initial flux linking with a coil is ϕ₁

ஃ Initial flux linkages = Nϕ₁ In time interval t, the flux linking with the coil changes from ϕ₁ to ϕ₂.

ஃ Final flux linkages = Nϕ₂

ஃ Rate of change of flux linkages = Nϕ₂ - Nϕ₁/t

Now as per the first law, e.m.f. will get induced in the coil and as per second law the magnitude of e.m.f. is proportional to the rate of change of flux linkages.

• With K as unity to get units of e as volts, do is change in flux, dt is change in time hence (dϕ/dt) is rate of change of flux.

• Now as per Lenz's law (discussed later), the induced e.m.f. sets up a current in such a direction so as to oppose the very cause producing it. Mathematically this opposition is expressed by a negative sign.

• Thus such an induced e.m.f. is mathematically expressed alongwith its sign as,

ஃ e = - N dϕ / dt volts

The total flux linkages of the coil are given by,

λ = Nϕ (WbT)

where N is the number of turns of the coil.

Hence induced e.m.f. can be expressed as,

e = - dλ/dt

The negative sign indicates that induced e.m.f. opposes the changes in the flux linkages, according to Lenz's law.

    ஃ  e = N dϕ/dt = dλ/dt

where sign of the 'e' must be determined by Lenz's law.

Ex. 1.21.1 The magnetic core in Fig. 1.21.1 is made from laminations of M-5 grain-oriented electrical steel. The winding is excited with a 60 Hz voltage to produce a flux density in the steel of B = 1.5 sin ?????? T, where ????? = 2π 60 rad/sec. The steel occupies 0.94 of the core cross-sectional area. The mass-density of the steel is 7.65 g/cm". Find :

i) The applied voltage, ii) The peak current, iii) The rms exciting current, and iv) The core loss The magnetic field intensity corresponding to B_max = 1.5 T is H_max = 36 A turns/m. AU : May-19, Marks 13

iv) Core loss density for M-5. grain oriented steel is 1.2 W/kg from the data sheet.

Core loss = 1.2 × 13.198 = 15.84 W

Review Question

1. State the Faraday's laws of electromagnetism.