Transcript Physics_A2_38_InductionLaws

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

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
North Anticlockwise
Induced south
pole
Induced North
Pole
Movement
South clockwise
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 = BIl
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 BIl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
= BIls / It
= Bl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 (Tm2) 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 :
= Bls /t
However, s /t is change in distance over change in
time.... i.e. Velocity, so the above equation can be rewritten :
= Blv