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 Electromagnetic Induction

What is Electromagnetic Induction?

 When the magnetic flux linking a conductor ( or coil ) changes , an e.m.f. is induced in the conductor . If the conductor ( or coil ) forms a complete loop , a current will flow in it . This phenomenon is called electromagnetic induction . 

 

What is Electromagnetic Induction?

Laws of Electromagnetic Induction

 Faraday's  First Law :-

When the magnetic flux linking a conductor or coil changes , an e.m.f. is induced in it . It does not matter how the change in magnetic flux is brought about . The essence of the first law is that the induced e.m.f. appears in a circuit subjected to changing magnetic field . Second law . 

 Faraday's second  Law :-

The magnitude of the e.m.f. induced in a conductor or coil is directly proportional to the rate of change of flux linkages .,

 

 

 

 Direction of Induced E.M.F. and Current 

The direction of induced e.m.f. and hence the current ( if the circuit is closed ) can be determined by one of the following two methods :

 ( i ) Lenz's law

 ( ii ) Fleming's right - hand rule 

( i ) Lenz's law . 

The induced current will flow in such a direction so as to oppose the cause that produces it .  Let us apply Lenz's law to . Here the N - pole of the magnet is approaching a coil of several turns . As the N - pole of the magnet moves towards the coil , the magnetic flux linking the coil increases . Therefore , an e.m.f. and hence current is induced in the coil according to Faraday's laws of electromagnetic induction . According to Lenz's law , the direction of the induced current 

 

 

will be such so as to oppose the cause that produces it . In the present case , the cause of the induced current is the increasing magnetic flux linking the coil . Therefore , the induced current will set up magnetic flux that opposes the increase in flux through the coil . This is possible only if the left hand face of the coil becomes N - pole . Once we know the magnetic polarity of the coil face , the direction of the induced current can be easily determined by applying right - hand rule for the coil

 

 

 It may be noted here that Lenz's law directly follows from the law of conservation of energy Le in order to set up induced current , some energy must be expended . In the above case , for example , when the N - pole of the magnet is approaching the coil , the induced current will flow in the coil in such a direction that the left - hand face of coil becomes N - pole . The result is that the motion of the magnet is opposed . The mechanical energy spent in overcoming this opposition is converted into electrical energy which appears in the coil . Thus Lenz's law is consistent with the law of conservation of energy . 

( ii ) Fleming's right - hand rule . 

This law is particularly suitable to find the direction of the induced e.m.f. and hence current when the conductor moves at right angles to a stationary magnetic field . It may be stated as under : Stretch out the forefinger , middle finger and thumb of your right hand so that they are at right angles to one another . If the forefinger points in the direction of magnetic field , thumb in the direction of motion of the conductor , then the middle finger will point in the direction of induced current .

 

Consider a conductor AB moving upwards at right angles to a uniform magnetic field as shown in Fig . 9.3 . Applying Fleming's right - hand rule , it is clear that the direction of induced current is from B to A. If the motion of the conductor is downward , keeping the direction of magnetic field unchanged , then the direction of induced current will be from A to B.

 

Fleming's Left Hand Rule : Fleming's left hand rule is applicable to d.c. motor for the direction of the mechanical force experienced . The rule states that if the fore finger , middle finger and the thumb of the left hand are mutually perpendicular to each other and the fore finger points towards the magnetic field . Middle finger points towards electric current and then the thumb gives the direction of force acting on the current carrying conductor .

 

 

Induced E.M.F. 

When the magnetic flux linking a conductor ( or coil ) changes , an e.m.f. is induced in it . This change in flux linkages can be brought about in the following two ways : ( i ) The conductor is moved in a stationary magnetic field in such a way that the flux linking it changes in magnitude . The e.m.f. induced in this way is called dynamically induced e.m.f. ( as in a d.c. generator ) . It is so called because e.m.f. is induced in the conductor which is in motion . ( ii ) The conductor is stationary and the magnetic field is moving or changing . The e.m.f. induced in this way is called statically induced e.m.f. ( as in a transformer ) . It is so called because the e.m.f. is induced in a conductor which is stationary . It may be noted that in either case , the magnitude of induced e.m.f. is given by Ndo / dt or derivable from this relation .

 

 

-Self Inductance and Mutual Inductance :

 Let us take a closed coil and current is supplied to the coil by a source , then it will produce a magnetic flux . Now with the variation of current , the flux will also change . This change of flux will produce an emf in the coil . This generated or induced emf is called the self - induced emf . Now the self inductance ( L ) of a coil is the characteristic or property of the coil , by which an emf is generated when the current is varied through the coil . It is denoted by ' L ' and the unit is Henry . It depends upon the shape of the coil used , square of the number of turns of the coil and neighbouring any magnetic material .

 

 

Mutual Inductance :

 Let us take a coil ' x ' which is placed close to other coil ' y ' . Now if the current of the coil ' x ' can be varied or changed , then an emf will be generated in coil ' y ' . The generated or induced emf in coil ' y ' exist so long as the current in the coil ' x ' changes , but not found when the current through coil ' x ' is steady . This is known as mutual induced emf . The mutual inductance of a coil is the characteristics or property of a coil by which an emf is generated in a coil when there is a variation or change of current through its nearby coil . It is denoted by ' M ' . The unit is Henry . It depends on the closeness of coil and the magnitude of the variation of current ,

 

 

Co - efficient of Self Induction : When the current in a coil changes , the magnetic field also changes and producing an induced emf in the particular coil . This process is known as self induction . The e.m.f. induced in the coil is directly proportional to the rate of change of current , the constant of proportionality is known as the co - efficient of self induction of the coil .

 
Concept of Eddy Current and Eddy Current Loss : 

Eddy Current :

We know that any rate of change of flux produces induced e.m.f. in the core , As Iron core is a conductor , an e.m.f. is also induced in the same manner in the core called eddy current . As the core is closed in itself a current will flow through the core is known as eddy current orcirculating current or faucault current . The magnetude of current depends on the value eddy current and the resistance of the eddy current path . Eddy Current Loss : The loss of electrical energy in the form of heat energy which may be produced by the flow of eddy current induced in the armature core , magnetic core material and the pole by changing e.m.fs is called eddycurrent loss or circulating current loss . We n.Bmax².f.2t2 x Volume of lamination = ( Where , n = Steinmetz constant a f = frequency of t = thickness of P ac fle Far = C

 

Eddy Current Loss : 

The loss of electrical energy in the form of heat energy which may be produced by the flow of eddy current induced in the armature core , magnetic core material and the pole by changing e.m.fs is called eddycurrent loss or circulating current loss . We = n.Bmax².f.²t² x Volume of lamination ( Where , n = Steinmetz constant f = frequency of reverasl t = thickness of lammation ) The eddy current loss may be reduced ( a ) laminations of the core ( b ) Lower the flux density , decrease the loss ( c ) choosing alloy for magnetic core eddycurrent loss is reduced .