Dynamically Induced EMF and Statically Induced EMF

1. Chandrashekhar S Patil
Sharad Institute of Technology
Polytechnic
Yadrav
Unit 1.5-Electric and Magnetic Circuits
(Dynamically Induced EMF& Statically Induced EMF-
Self induced EMF)

2. Contents:-
Sr No. Topic Slide Number
01. Induced EMF 4
02. Dynamically Induced EMF 5
03. Statically Induced EMF 6
04. Self Induced EMF 7
05. Magnitude and Coefficient of Self Induced
EMF
9 &10
2

3. Electromagnetic Induction
3
When the magnetic flux linking a conductor changes, an EMF is induced in
the conductor If the conductor forms a complete loop or circuit, a current will
flow in it. This phenomenon is known as “electromagnetic induction”.
Definition: The phenomenon of production of EMF and hence current in a
conductor or coil when the magnetic flux linking the conductor or coil
changes is called electromagnetic induction.

4. Induced EMF:
4
When the magnetic flux linking a conductor(or coil) changes, an EMF is
induced in it.This change in flux linkages can be brought about in following
two ways:
1. The conductor is moved in a stationary magnetic field in such a way
that flux linking it changes in magnitude. The EMF induced in this way
is called dynamically induced EMF(as in a DC generator).It is so called
because EMF is induced in the conductor which is in motion
2. The conductor is stationary and the magnetic field is moving or
changing. The EMF induced in this way is called statically induced
EMF(as in a transformer).It is so called because the EMF is induced in
a conductor which is stationary.
It may be noted that in either case the magnitude of induced EMF is
given by Nd§/dt

5. Dynamically Induced EMF
5
Consider a single conductor of length “l”meters moving at right angles
to a uniform magnetic field of B Wb /𝑚2
with a velocity of v m/s(as
shown in diagram). Suppose the conductor moves through a small
distance dx in dt seconds. Then area swept by the conductor is l*dx
According to Faradays law of
electromagnetic
electromagnetic induction the
magnitude of
induced EMF(e) induced in the
conductor is
given by:
Special case: If the conductor moves at an angle Ø the magnetic field then the velocity at
which the conductor moves across the field is v sinØ
e B lv sinØ
The direction of Induced EMF can be determined from Flemings Right Hand Rule.

6. Statically Induced EMF
6
When the conductor is stationary and the field is moving or changing . The
EMF induced in the conductor is statically induced EMF.
A statically induced EMF can be further sub-divided in to.
1. Self Induced EMF.
2. Mutually Induced EMF.
It is possible to change the number of lines of force linking with the coil and
therefore to induce an EMF in it even without resorting to its motion relative
to a magnetic field. Such an EMF is then designated as Statically Induced
EMF or a transformer EMF.
The flux linking with the coil may be its own flux produced by the current
flowing through it
or it may come from a neighbouring coil. The EMF’s induced in the coil by
variation of the flux in these two situations are respectively known as Self

7. Self Induced EMF
7
Figure shows a coil (C) having N turns connected in series with a switch
(Sw)a battery (B) and a variable resistor(R).
On closing the switch let the current in the coil be I amperes. The coil will
have its own flux threading through it due to the passage of this current.
The lines of force which form complete loops as indicated are said to be
linked with the coil.
If § Weber's is the resultant flux linking with the coil then the total flux
linkages (product flux*turns) will be N §.
If now the current flowing through the coil is changed by varying R, then the
number of lines of force linking with the coil will also change. Hence
according to Faradays Law of electromagnetic induction an EMF is induced
in the coil. This phenomenon is known as “Self Induction”.
The EMF induced in the coil is therefore called a self Induced EMF or EMF
of Self Induction.
This EMF lasts till the current in the coil is changing.
The phenomenon of self induction is most important in
Alternating current circuits since in these the current is
Changing from instant to instant The action of a choke used in
Fluorescent tube or filter circuit of a rectifier depends upon

8. Self Induction
8
A coil or a circuit in which a change of current causes an EMF of self
induction to be induced within the coil itself is said to have self inductance
or frequently just inductance.
 Due to this self inductance, when the current in the coil is increased, the
self induced emf in it will oppose this increase(Lenz Law) by acting in the
direction opposite to that of the applied EMF.
 Similarly if the current is decreased the self induced emf will tend to
keep the current at its original value by acting in the same direction
as the applied EMF.
 Thus any change in the current through the coil is opposed due to its self
inductance is sometimes called analogously called electrical inertia or
electromagnetic inertia.
The self inductance may therefore be defined as that property by

9. Magnitude of Self Induced EMF
9
 The magnitude of the self induced EMF in the coil C under consideration on
changing the current flowing through it is given by
 The minus sign in the above expression signifies that this emf is opposing the
change in current in the coil.
 If the flux of § Weber's is produced by the current of I amperes flowing through
the coil then we can write.
Total Flux linking with the coil
§= (Flux/Ampere) x Current in Amperes.
 §=(§/I )x I
 For any circuit so long as the permeability of the surrounding medium remains
constant the flux produced is proportional to the current so that § /I =constant.
 Therefore Rate of change of flux = §/I x Rate of Change of I
Substituting this in the above mentioned expression for the induced emf we
get
e=-N* §/I *Rae of Change of I
 The constant N§/I in the above expression is called the coefficient of self
induction or coefficient of self inductance and denoted by L. It is a
quantitative measure of self induction and is usually referred as self induction
or simply inductance of a coil or circuit.

10. Coefficient of Self inductance
10
The coefficient of self induction or coefficient of self inductance (L) of a
coil or circuit can therefore be defined as the flux linkages (in weber
turns)per ampere current in it.
L= N§/I
The unit of inductance is henry(H) in the above equation of N§=1 Wb-
turn, I = 1A then L = 1H.
Now substituting L= N§/I in the previous equation we have
e=- L * Rate of change of the current.
With usual calculus equation this can be written as
e=-Ld§/dt volts.
Hence coefficient of self induction or coefficient of self
inductance(L) of a coil or circuit can also be defined as equal to the
emf induced in volts when the current in the circuit changes
uniformly as the rate of one ampere per second.
Alternatively: A circuit has an inductance of one henry when a current
changing uniformly at the rate of one ampere per second induces an
opposing emf of I volt in it

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