6 Electromagnetic
Induction
snap sHOTS
Electric currents in closed circuit, are induced so as to oppose the changing magnetic
a
field. This is as per the law of conservation of energy. In case of an open circuit, an emf
is induced across its ends.
The polarity of the induced emf is such that it tends to produce a current which opposes
the change in magnetic flux that produces it. This is Lenz's law.
Eddy currents are basicaly the induced currents set up inside the body of conductor
whenever the magnetic flux linked with it changes.
Eddy currents tend to follow the path of least resistance inside a conductor. So they
form irregularly shaped loops. However, their directions are not random, but guided
by Lenz's law.
Eddy currents have both undesirable effects and practically useful applications
Eddy currents can be induced in biological tissues. For example, the cavity of the eye
is filled with a conducting fluid. A large transient magnetic field of 1 T alternating at
a frequency of 60 Hz then induces such a large current in the retina that it produces a
sensation of intense brightness.
The retarding force due to the eddy current inhibits the motion of a magnet. This
phenomenon is known as electromagnetic damping
Inductance is a measure of the ratio of induced flux o to the current I.
Inductance is a scalar quantity having the dimensions of magnetic flux divided by
current. Its dimensions in terms of the fundamental quantities are [ML2T-2A-2]. Its SI
unit is Wb A-l or VsA*l which is called henry (H).
Inductance is named in honour of Joseph Henry who discovered electromagnetic
induction in USA independently of Faraday in England.
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mtG Objective NCER
Inductance plays the role of electrical inertia. The analogue of self-inductance in mechanics is mass.
A solenoid made from a thick wire has a negligible resistance but a suficiently large self-inductance. Such an an
element is called ideal inductor, denoted by - r
A wire itself cannot act as an inductor because the magnetic fux linked with the wire of negligible cross-sectional
wire bent into the form of
area is zero. Only a a coil can act as an inductor. Moreover, the
self-induced em
n
appears only during the time, the current through it is changing.
The inductance of a coil depends on its geometry and the intrinsic properties of the material that fills up the
space inside it. In this sense, it bears similarly to capacitance and resistance. The capacitance of a
paralle
plate capacitor depends on the plate area and plate separation (geometry) and the dielectric constant K of the
interposing medium (intrinsic material properly). Similarly, the resistance ofa conductor depends on its length
and cross-sectional area
(geometry) and resistivity (intrinsic material property)
The capacitance, resistance, inductance and diode constitute the four passive elements of an electrical circuit.
In fact, these are the four alphabets of electrical/electronic
engineering
When two coils are inductively coupled, in addition to the emf produced due to mutual induction, induced
emf is set up in the two coils due to self induction also.
The mutual inductance of two coils is a property of their combination. The value of M remains
unchanged
irrespective of the fact that current is passed through one coil or the other.
Mutual inductance of two coils is numerically equal to magnetic flux linked with one coil, when a unit current
flows through the neighbouring coil.
While calculating the mutual inductance of two co-axial solenoids of different lengths, the length of the larger
solenoid is to be considered.
A rectangular coil moves linearly in a field when coil moves with constant velocity in a uniform magnetic field
flux and induced emf will be zero.
An emf is induced in the following cases:
When a train moves horizontally in any direction.
When an aeroplane flies horizontally.
When a conductor falls freely in east-west direction.
When an aeroplane takes off or lands with its wings in east-west direction.
The plane of orbit of a metallic satellite is inclined to the equatorial plane at any angle.
When a magnet is moved with respect to a coil, an emf is induced in the coil.
When a current carrying coil is moved with respect to a stationary coil, a current is induced in the stationary
coil.
When strength of current flowing in a coil is increased or decreased induced current is developed in the col
in same or opposite direction.
In an ac generator, mechanical energy is converted to electrical energy by virtual of electromagnetic
induction.
REVIEW FORMULAE
Self-inductance of long solenoid
Magnetic flux, o=BA cos BA
L=
Induced emf, e=-N 4
Average induced emf, e=-N % where n 7
Induced current, I = Mutual inductance of two closely wound solenoids,
R
The emf induced in a conductor of length l moving M=
with velocity v perpendicular to field B, E = Blv.
Induced emf developed betwen the two ends of rod
where n
rotating at its one end in perpendicular magnetic
feld eBfo Coefficient of coupling K= M
Combination ofinductances L = L +L2
NBA@, where = 2tuD
e Li and L2 are
Two inductors of self-inductance
Maximum induced current, I,= connected in series L = Ly + L2 t 2M
Two inductors of self-inductors L and Lz are
For self-induction, =LI
connected in parallel
Self induced emf, e=-L
L- or
For mutual induction, 9 = MI
L+
Mutual induced emf, e = - M d Energy stored in an inductor U=LI?
dt
