Book Reference : Pages 123-126Book Reference : Pages 123-126

1.1. To understand the direction of induced To understand the direction of induced currents and their associated fieldscurrents and their associated fields

2.2. To introduce the terms magnetic flux and To introduce the terms magnetic flux and magnetic flux linkagemagnetic flux linkage

3.3. To be able to calculate the size of the To be able to calculate the size of the induced EMF for a given generator induced EMF for a given generator arrangementarrangement

When an electric current is passed through a coil of wire, When an electric current is passed through a coil of wire, a magnetic field is formed around the coil in much the a magnetic field is formed around the coil in much the same way as a permanent bar magnetsame way as a permanent bar magnet

We need another We need another “rule” “rule” to to allow us to determine which allow us to determine which end is north and southend is north and south

NNorth Aorth Annticlockwiseticlockwise South clockwiseSouth clockwise

Looking Looking intointo the coil the coil

When a magnet is introduced into a coil an electric When a magnet is introduced into a coil an electric current is induced. This current in turn creates a current is induced. This current in turn creates a magnetic field around the coil. If the magnet is moved in magnetic field around the coil. If the magnet is moved in the opposite sense, the direction of the induced current the opposite sense, the direction of the induced current & resulting field reverse.& resulting field reverse.

But which way?But which way?

Consider a north pole entering a coil, there are two Consider a north pole entering a coil, there are two possibly scenarios....possibly scenarios....

The induced current could form a The induced current could form a southsouth pole at this end? pole at this end?The induced current could form a The induced current could form a northnorth pole at this end? pole at this end?

Try to reach a conclusion based upon pole attraction / Try to reach a conclusion based upon pole attraction / repulsion and the conservation of energy repulsion and the conservation of energy

Lenz’s law states that :Lenz’s law states that :The direction of the induced current is always such as to The direction of the induced current is always such as to oppose the change which has caused the current to be inducedoppose the change which has caused the current to be induced

Movement

Induced North Pole

Induced south pole

NNorth Aorth Annticlockwiseticlockwise

South clockwiseSouth clockwise

Looking

Looking in

toin

to th

e co

il

the

coil

Looking

Looking in

toin

to th

e co

il

the

coil

We can then simply use the We can then simply use the “Solenoid rule” “Solenoid rule” to establish the direction of the induced to establish the direction of the induced currentcurrent

Consider a conductor of length Consider a conductor of length ll (which is part of a (which is part of a complete circuit), cutting through a magnetic field with a complete circuit), cutting through a magnetic field with a flux density of B. There is an induced current I flowing in flux density of B. There is an induced current I flowing in the circuit.the circuit.

The conductor will experience a force given by F = BIThe conductor will experience a force given by F = BIll

An equal & opposite force must be applied to keep the An equal & opposite force must be applied to keep the conductor moving and if the conductor is moved a conductor moving and if the conductor is moved a distance distance s then the work done by this force is Fs then the work done by this force is Fss

The work done can be expanded to BIThe work done can be expanded to BIllss

If the current I has been flowing for If the current I has been flowing for t seconds then the t seconds then the charge transferred is: Q = Icharge transferred is: Q = Itt

If we consider EMF If we consider EMF (Voltage) (remember potential (Voltage) (remember potential difference is the work done per unit charge)difference is the work done per unit charge)

= W/Q = W/Q = BI= BIlls / s / IIt t = B= Blls /s /tt

The conductor of length The conductor of length l l has moved through a distance has moved through a distance s, this gives us an area A :s, this gives us an area A :

= = BA /BA /t t

This equation can be extended in two ways. Firstly if we This equation can be extended in two ways. Firstly if we have a coil with N turns then the have a coil with N turns then the Magnetic flux linkage Magnetic flux linkage becomes becomes

NN=NBA (often written N=NBA (often written N=BAN)=BAN)

This assumes that the coil and magnetic field are This assumes that the coil and magnetic field are perpendicular.perpendicular.

When the coil is parallel to the field, the flux linkage When the coil is parallel to the field, the flux linkage is zero since no field lines pass through the coilis zero since no field lines pass through the coil

If the coil is reversed the magnetic flux linkage is If the coil is reversed the magnetic flux linkage is reversed and becomes -BANreversed and becomes -BAN

The general case is when the magnetic field is at an The general case is when the magnetic field is at an angle angle to the normal. The flux linkage is then given by: to the normal. The flux linkage is then given by:

NN=BAN cos =BAN cos

Faraday’s law of electromagnetic induction :Faraday’s law of electromagnetic induction :

The induced EMF in a circuit is equal to the rate of The induced EMF in a circuit is equal to the rate of change of flux linkage through the circuitchange of flux linkage through the circuit

= -N= -N / /t t

The minus sign indicates that the induced EMF is in such The minus sign indicates that the induced EMF is in such a direction as to oppose the change causing ita direction as to oppose the change causing it

From the last equation our induced EMF will have From the last equation our induced EMF will have derived units of Webers sderived units of Webers s-1-1 which is equivalent to which is equivalent to Volts(V)Volts(V)

Webers can therefore be thought of as a “volt second”Webers can therefore be thought of as a “volt second”

To induce a current we need changing flux linkage which To induce a current we need changing flux linkage which can be provided by either :can be provided by either :

1.1. Permanent magnet (physically move either the Permanent magnet (physically move either the magnet or the wire (coil) (dynamo)magnet or the wire (coil) (dynamo)

2.2. Electromagnet : The field provided can be Electromagnet : The field provided can be changed by changing the supplied current (A changed by changing the supplied current (A transformer! Couple of lessons time)transformer! Couple of lessons time)