PPT No. 29
* Electromotive Force
* Motional emf
* Lenz’s law
Electromotive Force
Definition of emf
Electromotive force (emf) is a source of energy that
maintains a potential difference between different points
in an electrical circuit or a device or a conductor
and can cause an electric current to flow in it.
emf is a measure of the work done per unit charge
by a source in moving an electric charge or
creating a separation of positive from negative charges,
thereby creating a voltage difference.
Electromotive Force
emf is the rate at which energy is drawn from the source
when unit current flows through the circuit or device.
The word "force" in "electromotive force" is a misnomer.
Electromotive force is not really a force.
emf has the dimensions of energy per charge.
Electromotive force is often denoted by
or ℰ (script capital E).
The unit of emf in SI system is volt
which is equivalent to joule /coulomb.
Types of Voltage
There are two types of voltage as follows
Electrostatic potential due to
(configuration / position of) stationary charges
Here Ecs or E is the electrostatic field intensity created by
the charge separation associated with the emf,
dℓ is an element of the path from terminal A to terminal B.
Electromotive Force
This equation is applicable only to terminals A and B and
Not to the paths between points A and B.
Electrostatic energy is conserved during a cyclic process
within the associated system.
The system is conservative or irrotational (i.e., the work
done against the field around a closed path is zero).
Its sources obey the equation
where
Electromotive Force
Electromotive force due to moving charges:
When magnetic field varies, emf is "induced "
around a stationary closed path C
the integral is around an arbitrary, stationary closed curve C
surrounding a region of varying magnetic field.
E is the entire electric field- electrostatic (conservative)
and field due to
changing magnetic flux density (nonconservative).
Electromotive Force
Out of the two origins, the electrostatic field
does not contribute to the net emf around a circuit.
In the case of the contribution due to changing magnetic flux
there is transfer of energy in a cyclic process
in the associated system (e. g. magnetic field in a coil).
The field is described by curl sources and
its divergence is zero.
Devices and Mechanisms producing emf
Devices that produce emf have
different mechanisms/ principles e.g.
* Electrical generators, Transformers (electromagnetic induction)
* Voltaic cells (chemical reactions),
* Thermocouple devices (electricity by thermal gradient),
* Solar cells (electricity by light energy),
* Piezoelectric (electricity by mechanical pressure) etc.
Electromotive Force by Magnetic Induction
Electromotive force is induced in a coil or conductor
whenever there is a change in the magnetic flux linkages.
Depending on the way
in which the changes are brought about,
there are two types of induced emf as follows
* Motional emf
* Transformer emf
Types of Induced emf
When the change in the magnetic flux linkage
is brought about by moving a conductor
in a stationary magnetic field,
the electromotive force generated by
motion of conductor is referred to as Motional emf.
When the change in flux linkage arises from a change
in the magnetic field around the stationary conductor,
the electromotive force generated by a time-varying
magnetic field is referred to as Transformer emf.
Motional emf
Motional emf is the emf generated
due to the motion of a conductor in
a magnetic field which does not vary in time.
It is one of the two types of emf
(other is Transformer emf)
which obey the same law –
Faraday’s Law of Electromagnetic Induction
and follow the Flux Rule.
Motional emf in terms of Moving Rod Parameters
Fig. (a) Metal rod moving through a magnetic field
(b) Forces acting on the electron in the rod
Motional emf in terms of Moving Rod Parameters
Motional emf can be expressed in terms of
moving rod parameters and magnetic flux as follows
Consider a thin metal rod
moving with a constant velocity v
through a magnetic field B.
Each conduction electron (having charge e) in the rod,
experience a magnetic force given by Lorentz force law.
It has magnitude evB and direction perpendicular
to both their motion and the field.
This force pulls electrons towards one end of the rod.
Motional emf in terms of Moving Rod Parameters
Motional emf in terms of Moving Rod Parameters
Electrons move under the influence of the magnetic force
and other interactions. It produces a charge separation
which sets up an electric field E that exerts a force eE
An equilibrium is soon established in which
the electric and magnetic forces balance each other.
For an electron inside the rod (not at the ends)
the electrostatic and magnetic forces balance, so
e E = evB .
Hence the magnitude of the electric field is E = vB
Motional emf in terms of Moving Rod Parameters
The potential difference (V) between two points separated
by a distance l and the magnitude of
the average electrostatic field are related thus: E = V/ l
By comparing the two expressions for the electric field,
a relation for the voltage is
V = vBl.
In the case where there is no current flow,
the potential difference must be equal to the emf
emf ℰ = vBl . ...
Magnetic Flux and Rod Parameters
Suppose a conducting rod of length ℓ
slides to the right with the constant velocity v
along a U-shaped conducting frame
in the presence of a uniform magnetic field B.
The magnetic flux φB linked to the circuit
is the product of
the perpendicular component of magnetic field-strength, B,
and the area of the circuit, ℓx,
where x is the position of the sliding rod.
Magnetic Flux and Rod Parameters
If the rod moves a distance
in a time interval dt, then in the same time interval
the magnetic flux linking the circuit increases by
dφ/ dt = Bℓv
Thus, the emf generated in the circuit by moving a rod
is the product of the magnetic field-strength,
the length of the rod, and the velocity of the rod.
Applications of Motional emf
The voltage due to motional emf can be seen to be
the work done per unit charge.
Motional emf is a good example of how mechanical energy,
energy associated with motion,
can be transformed to electrical energy e.g.
In electrical generators a conductor (coil)
is moved through a magnetic field and emf is generated.
emf is induced between the wingtips of the airplane
as the plane flies through the Earth's magnetic field
Lenz’s Law
Statement of the Lenz’s Law
Faraday's law of electromagnetic induction does not state
anything about the direction of the induced current.
The direction of induced emf and current is given by
Lenz's law. The statement of the law is as follows:
An induced current in a closed conducting loop always flows
in such a direction that it opposes the change that produces it.
Thus the induced emf (effect) and
the change in the magnetic flux (cause) have opposite signs.
Lenz’s Law- Explanation
When an emf is generated by
a change in magnetic flux according to Faraday's Law,
the polarity of the induced emf is such that
it produces a current whose
magnetic field opposes
the change which produces emf.
Lenz’s Law- Explanation
Inside any loop of wire
the induced magnetic field is such that
it always acts to keep the magnetic flux in the loop constant.
If the B field is increasing,
the induced field acts to oppose the increase.
If B is decreasing,
the induced field acts in the direction
to oppose the decrease
Lenz’s Law- Explanation
Suppose that a magnet is moved towards a conducting loop.
Magnetic flux ϕB through the loop increases to the left.
The current is induced in a direction such that
the magnetic field due to the induced current is to the right &
opposes/ reduces, the original increase in flux.
If the magnet is moved out, the induced current and
induced magnetic field reverse direction
Lenz’s Law
(a )
(b)
a) N pole pushed in=>
applied field B increases by dB to left.
b) Current i is induced in Anticlockwise direction
c) Binduced points to right
(c)
Lenz’s Law
Lenz’s law is a particular case of
a very general principle in PhysicsLe Chatelier’s Principle –
A physical system always reacts to any change
that is impressed upon it from outside.
Lenz’s Law- Explanation
Suppose a magnet is moved in
The vicinity of a closed conducting coil, then
Magnetic field B,
Change (increase/ decrease) in the magnetic field ΔB,
induced field Binduced and
induced current Iinduced
due to various movements of magnet are as follows
Lenz’s Law
Fig. A stationary conducting coil with a bar magnet showing
Current I, B-Field, ΔB, Binduced for movements of the magneta) N pole moved towards coil b) N pole moved away from coil
c) S pole moved Away from coil d) S pole moved Towards coil
Lenz’s Law
A stationary conducting coil with a bar magnet showing
Current I, B-Field, ΔB, Binduced for movements of the magneta)N pole pushed towards coil
=> Applied field B increases by
ΔB to left.
Binduced points to right
b) N pole pulled away =>
Applied field B decreases by
ΔB to right.
Binduced points to left
c) S pole pulled away =>
Applied field B decreases by
ΔB to left.
Binduced points to right
d) S pole pushed towards =>
Applied field B increases by
ΔB to right.
Binduced points to left
Lenz’s Law
Fig. A stationary conducting loop with a bar magnet showing
Binduced & Iinduced are in opposite directions for opposite movements
(a) and (b) of the magnet as follows
a) N pole moved towards loop b) N pole moved away from loop
Lenz’s Law
Fig. A stationary conducting loop with a bar magnet showing
Binduced & Iinduced are in opposite directionsfor opposite movements
in (c) and (d) of the magnet as follows
c) S pole moved towards loop d) S pole moved away from loop
Lenz’s Law
A stationary conducting loop with a bar magnet showing Binduced &
Iinduced are in opposite directions for opposite movements of the magnet
a)N pole pushed towards loop
=> Applied field B increases by
ΔB downward.
Binduced points upward
Iinduced flows Anticlockwise
b) N pole pulled away from loop
=> Applied field B decreases by
ΔB upward.
Binduced points downward
Iinduced flows clockwise
c) S pole pushed towards
loop => Applied field B
decreases by ΔB upward
Binduced points downward
Iinduced flows clockwise
d) S pole pulled away from
loop => Applied field B
increases by ΔB downward.
Binduced points upward
Iinduced flows Anticlockwise