# Book Reference : Pages 123-126 1.To understand the direction of induced currents and their associated fields 2.To introduce the terms magnetic flux and.

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Book Reference : Pages 123-126 1.To understand the direction of induced currents and their associated fields 2.To introduce the terms magnetic flux and magnetic flux linkage 3.To be able to calculate the size of the induced EMF for a given generator arrangement

When an electric current is passed through a coil of wire, a magnetic field is formed around the coil in much the same way as a permanent bar magnet We need another “rule” to allow us to determine which end is north and south North Anticlockwise South clockwise Looking into the coil

When a magnet is introduced into a coil an electric current is induced. This current in turn creates a magnetic field around the coil. If the magnet is moved in the opposite sense, the direction of the induced current & resulting field reverse. But which way? Consider a north pole entering a coil, there are two possibly scenarios.... The induced current could form a south pole at this end? The induced current could form a north pole at this end? Try to reach a conclusion based upon pole attraction / repulsion and the conservation of energy

The induced current could form a south pole at this end? If this were to happen the north end of the magnet would be attracted and would be accelerated into the coil which would increase the size of the current and associated field would increase which in turn would increase the attraction and hence acceleration...... Energy would be created for free which breaks the law of energy conservation The induced current could form a north pole at this end? The north end of the magnet would be repelled by the induced north pole. External work must be done to overcome this repulsion. We have induced energy into the coil but we have also done work to overcome repulsion. Energy is not created and is conserved Energy is not created and is conserved

Lenz’s law states that : The direction of the induced current is always such as to oppose the change which has caused the current to be induced Movement Induced North Pole Induced south pole North Anticlockwise South clockwise Looking into the coil We can then simply use the “Solenoid rule” to establish the direction of the induced current

Consider a conductor of length l (which is part of a complete circuit), cutting through a magnetic field with a flux density of B. There is an induced current I flowing in the circuit. The conductor will experience a force given by F = BI l An equal & opposite force must be applied to keep the conductor moving and if the conductor is moved a distance  s then the work done by this force is F  s The work done can be expanded to BI l  s

If the current I has been flowing for  t seconds then the charge transferred is: Q = I  t If we consider EMF  (Voltage) (remember potential difference is the work done per unit charge)  = W/Q = BI l  s / I  t = B l  s /  t The conductor of length l has moved through a distance  s, this gives us an area A :  = BA /  t

The product (BA) of the magnetic flux density (B) and the area (A) is called the magnetic flux (  )  =BA Magnetic flux has the derived units of (Tm 2 ) and is given the special unit Weber (Wb) The induced EMF in our example is equal to the magnetic flux cut through per second  =  /  t

This equation can be extended in two ways. Firstly if we have a coil with N turns then the Magnetic flux linkage becomes N  =NBA (often written N  =BAN) This assumes that the coil and magnetic field are perpendicular. When the coil is parallel to the field, the flux linkage is zero since no field lines pass through the coil If the coil is reversed the magnetic flux linkage is reversed and becomes -BAN

The general case is when the magnetic field is at an angle  to the normal. The flux linkage is then given by: N  =BAN cos  Faraday’s law of electromagnetic induction : The induced EMF in a circuit is equal to the rate of change of flux linkage through the circuit  = -N  /  t The minus sign indicates that the induced EMF is in such a direction as to oppose the change causing it

From the last equation our induced EMF will have derived units of Webers s -1 which is equivalent to Volts(V) Webers can therefore be thought of as a “volt second” To induce a current we need changing flux linkage which can be provided by either : 1.Permanent magnet (physically move either the magnet or the wire (coil) (dynamo) 2.Electromagnet : The field provided can be changed by changing the supplied current (A transformer! Couple of lessons time)

A moving conductor in a field will have an induced emf providing the conductor cuts through the field lines We saw earlier that this can be given by :  = B l  s /  t However,  s /  t is change in distance over change in time.... i.e. Velocity, so the above equation can be re- written :  = B l v

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