MOTIONAL EMF
Consider a straight conductor moving in a uniform and time independent
magnetic field.
Blv ➔motional emf
Here the magnetic flux enclosed by the loop PQRS will be
Explanation of motional emf using Lorentz force
Consider any arbitrary charge q on the conductor PQ.When the rod moves with
a speed v in the magnetic field B,the charge also moves with speed v.Force on
charge is directed towards Q.Work done in moving charge from P to Q
W=FXl
= Bqv X l
Emf which is the work done per unit charge
𝐵𝑞𝑣𝑙
W= = Blv
𝑞
Induce EMF between the ends of the conducting rod which is rotated in a
magnetic field
Consider a conducting rod OQ of
length R rotating about O with a
constant angular velocity ω,in a
plane perpendicular to a
uniform magnetic field of flux
density B.If the rod may be
divided into elements of length
dr,the linear speed v of an
element at a distance r from O is
given by v = rω .Induced emf dE=
That is;
Bvdr
𝟏
=Brωdr E = 𝟐Bω𝑹𝟐
𝑅
Total emf E = ∫ 𝑑𝐸 =∫0 𝐵𝜔𝑟𝑑𝑟
𝑅2
= Bω 2
MUTUAL INDUCTION
When current flowing in one of two nearby coils is changed, the magnetic flux
linked with the other coil changes, due to which an emf is induced in the other
coil. This phenomenon of electromagnetic induction is called mutual induction.
The coil in which current is changed is called the primary coil, and the coil in
which current is induced is called the secondary coil.
MUTUAL INDUCTANCE / COEFFICIENT OF MUTUAL INDUCTION
Magnetic flux linked with the secondary coil α current in the primary coil
ΦαI
Φ=MI
This proportionality constant M is called mutual inductance.
EXPRESSION FOR MUTUAL INDUCTANCE OF TWO LONG COAXIAL SOLENOIDS
OF SAME LENGTH WOUND OVER THE OTHER
Consider 2 long coaxial solenoids each of length l.
n1 => No of turns /unit length of inner solenoid
n2=>No of turns / unit length of outer solenoid
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In an experimental arrangement of two coils C1 and C2 placed coaxially parallel
to each other, find out the expression for the emf induced in the coil C1 (of N1
turns) corresponding to the change of current I2 in the coil C2 (of N2 turns).
Limitations of Mutual Inductance
• The most significant disadvantage of mutual inductance is that leakage of the
inductance of one coil can cause the operation of another coil that is utilising
electromagnetic induction.
• To reduce leakage, electrical screening must be installed.
• The amount of mutual inductance between two coils in a circuit is determined
by the relative positions of the coils in the circuit.
SELF INDUCTION
Whenever the electric current passing through a coil or circuit changes, the
magnetic flux linked with it will also change. As a result of this, in accordance
with Faraday’s laws of electromagnetic induction, an emf is induced in the coil
or the circuit which opposes the change that causes it. This phenomenon is
called ‘self-induction’ and the emf induced is called back emf, current so
produced in the coil is called induced current.
SELF INDUCTANCE OF A LONG SOLENOID
A solenoid is a long coil of iron on which there are a large number of turns of
insulated wire, which when current is conducted through it results in the
production of a magnetic field. When current is carried by a coil, it has the
feature of self-inductance, which is the resistance or opposition to the change
in current that occurs while the current is carried by the coil. This occurs mostly
as a result of the self-induced emf created by the coil itself during operation.
We’ll use the example of a solenoid with N turns, length l, and cross sectional
area A as our example. It contains a current (I). If B denotes the magnetic field
at any point inside the solenoid, then magnetic flux indicated as –
So, the total magnetic flux associated with the solenoid may be calculated as
the product of magnetic flux through each turn and the total number of turns in
the solenoid.
a) Obtain the expression for the magnetic energy stored in a solenoid,
due to the current I flowing in it, in terms of magnetic field B, area of cross-
section A and length l of the solenoid.
(b) How is this magnetic energy per unit volume compared with the
electrostatic energy per unit volume stored in a parallel plate capacitor ?
