Electromagnetic Induction Basics

7/24/2019 Electromagnetic Induction Basics

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ELECTROMAGNETIC INDUCTION BASICS

The e.m.f is induced in the coil, when the there is a change in the flux linking with the coil.

This e.m.f. exists so long as the change in the flux exists.

Stationary flux will never induce any e.m.f. in a stationary conductor, even though it is stron( the e.m.f. is stronger when the magnet is closer to the conductor [seefig.(a) and fig.(b)] &is strongest (Em) when the conductor is perpendicular to the magnetic field).

Example:

fig.(a).Stronger e.m.f .induced in fig.(b). Lesser e.m.f.induced in

comparison of the position in fig.(b) comparison of the position in fig.(a)

G Galvanometer

ABInitial position of the magnet (closer to the conductor coil) in which the e.m.f. induced isstronger than in position CD

CDnew position of magnet moved away from conductor coil causing lesser e.m.f. to induce

than that in position AB.

The magnitude of this induced e.m.f. (and hence the amount in the deflection in thegalvanometer ) depends on the quickness of the movement

It is also found that if the conductor is moved parallel to the direction of the lines of flux (so

that it cuts none of these lines), then no e.m.f. is induced.

FARADAYS LAW OF ELECTROMAGNETIC INDUCTIONFirst Law

It states :-

When the magnetic flux linked with a circuit changes, an e.m.f. is always induced in it.or

Whenever a conductor cuts across magnetic lines of flux, an e.m.f. is induced in that

conductor.

Lenzs Law:

It states that ,

the electroma-

gnetically

induced current

always flow in

such a direction

that the action

of the magneticfield set up by it

opposes the

very cause

which produc-

es it . Thus,

a minus sign isgiven to theright-hand sideexpression (i)

Flux Direction

Conductor is perpendicular to the flux

induces strongest flux in the coil


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Second LawIt states :-

The magnitude of the induced e.m.f. is equal to the rate of change of flux linkage.

Example:Suppose a coil hasN turns and flux through it changes from an initial value

of 1Wb to the final value of 2Wb in time t seconds. Now, we know

Total flux linked = turns in the conductor coil flux linked with coil

Thus,Initial flux linkages = N1; Final Flux linkages =N2

Induced e.m.f. e=21

volt or e = N

21

volts

Putting the above expression in its differential from, we get

e =

() or e =N

volts=N

volts......equation (i)

CONCEPTS OF ALTERNATING EMF,VOLTAGE AND CURRENT

Omega() - It is angular velocity of the coil rotating in the magnetic fieldexpressed in radians / seconds.

Angular frequency () = 2f radians / secondswhere, f frequency in Hertz (Hz)

Maximum flux mis linked with coil when its plane coincides with the X-axis.

It is given as,

Maximum flux linked with coil (m) =BmA ......equation (ii)where, Bm maximum flux density in Wb/m

2

A area of the coil in m2

The value of the voltage generated ( in the coil rotating in the magnetic field ) depends uponthe number of turns in the coil(N), strength of the field ( i.e. flux (B)) and the speed at which

the coil or magnetic field rotates (expressed in radians / seconds ()).

......Statement 1

EQUATIONS OF THE ALTERNATING VOLTAGES AND CURRENTS

Consider a rectangular coil having N turns rotating in a uniform magnetic field with an

angular velocity of radian/second as shown infig.(c). Let time be measured from the X-ax

Maximum flux mis linked with the coil when its plane coincides with the X-axis( i.e. coil iperpendicular to the flux.

In time t seconds, this coil rotates through an angle = t. In this deflected position, the component of the flux which is perpendicular to the plane of th

coil is = m cost

fig.(c)

Y

X

= t

a

bc

mcos

m

mcos

msin

fig.(d)


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Explanation offig.(d):

sin(aco ) = sin =side ac /side ao ...... sin =

= side ac/m

side ac = msin = m sin t= side ob ....= t

cos(aco ) = cos =side oc/side ao ...... cos =

=side oc / m

side oc = m cos = m cos t =side ab ....= t

Hence, flux-linkages of the coil in this deflected position(i.e. when = t) are

(flux linkages, when = t) N=Nm cost

According to Faraday's Laws of Electromagnetic Induction, the e.m.f. induced in the coil isgiven by the rate of change of flux-linkages of the coil. Hence, the value of the induced e.m.

at this instant (i.e.when = t) or the instantaneous value of the induced e.m.f. is

e =

(N) volt ........from equation(i)

=

N

(m cos t) volt

= Nm (sin t) volt

= Nm sint

e = Nm sinvolt ........equation(iii)

When the coil has turned through 90 i.e. when = 90, then sin = 1, hence e has maximumvalue, say Em . Therefore, from equation(iii) ,we get

Em = Nm volt ........equation(iv)

= NBmA volt .........from equation (ii)

= 2f N BmA volt

where , , Bm maximum flux density in Wb/m2

A area of the coil in m2

f frequency of rotation of the coil in revolutions / second ( Hertz (Hz))

Substituting this value of Em (= Nm ..... from equation (iv)) in equation( iii), we get

e = Em sin= Em sint

Similarly, sinusoidal alternating current induced by this e.m.f. is expressed as follows :

i = Im sin = Im sint

PHASE DIFFERENCE

Consider three similar single-turn coils displaced from each other by angles and

and

rotating in a uniform magnetic field with the same angular velocity [fig.(e)]

fig.(e) fig.(f)


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In this case, the values of e.m.f.s induced in the three coils, are the same, but these coils donot reach their maximum or zero values simultaneously, rather one after another as shown in

fig.(f).

It is seen that curvesBand Care displaced from curveA by angles and (+) respective

Hence, it means that phase difference between A andB isand betweenB and Cis but

betweenA and C is (+ ) A leading alternating quantityis one which reaches its maximum or zero value earlier as

compared with the other quantity.

A lagging alternating quantityis one which reaches its maximum or zero value later than tother quantity.

For example , infig.(f),Blags behindAby and Clags behindAby (+ ). The three equations for the instantaneous induced e.m.f.s are :

eA= Emsin teB= Emsin ( t )eC= Emsin [t (+)]

In fig.(g), quantityB leads Aby an angle . Hence, their equations are

vA = Vm sin t ; vB = Vm sin (t + )

A plus (+) sign when used in connection with phase difference denotes 'lead' whereas a minu(-) sign denotes 'lag'

fig.(g)

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Electromagnetic Induction Basics