Download B . A = BA - RAJEEV Classes

When a conductor is moved across a magnetic field , an
electromagnetic force(emf) is produced in the conductor.
Electromagnetic induction is the production of an electromotive force
that results from the movement of a conductor through a magnetic field.
An electromotive force also results from the changing of magnetic flux in
a closed loop circuit.
Magnetic
Flux
The magnetic flux (often denoted Φ or ΦB) through a surface is the
surface integral of the normal component of the magnetic field B passing
through that surface.
The SI unit of magnetic flux is the weber (Wb).
The CGS unit is the maxwell .
Equation is given by, foe non uniform B
If B is uniform then equation becomes :
= B . A = BA
Faraday’s Laws Any change in the magnetic environment of a coil of wire will cause a
of
voltage (emf) to be "induced" in the coil. No matter how the change is
Electromagnetic produced, the voltage will be generated.
Induction
Equation for single loop
For N number of loop
Lenz law
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According to this law, If an induced current flows, its
direction is always such that it will oppose the change
which produced it.
Faraday’s 2nd law is also known as law of EMI
Law of EMI
The magnitude of induced emf is equal to the rate of change of flux
linkages with the coil.
e=
Emf induced in a straight conductor in uniform
magnetic field
When a straight conductor is moved through a magnetic field an e.m.f. is
induced between its ends. This movement must be in such a direction
that the conductor cuts through the lines of magnetic flux, and will be a
maximum when it moves at right angles to the field.
E = BLvsinθ
In general
d = (V
B) . L
Coil rotation
Coil rotation in magnetic field
A coil of N turns and area A being rotated at a constant angular
velocity θ in a magnetic field of flux density B, its axis being
perpendicular to the field.
Therefore the e.m.f E generated between the ends of the coil is:
E = -d(φ)/dt = - d(BANcosθ)/dt
E = BANωsinθ = BANωsin(ωt)
Self induction and Self inductance
Self inductance is defined as the induction of a voltage in a currentcarrying wire when the current in the wire itself is changing. In the case
of self-inductance, the magnetic field created by a changing current in
the circuit itself induces a voltage in the same circuit.
Unit is Henry
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Coefficient of self inductance
L=
s/
i
L depend only on
Shape of the loop
Medium
Self induced emf E is
Mutual induction
and
mutual
inductance
Mutual induction
The production of an electromotive force in a circuit by a change in
the current in an adjacent circuit which is linked to the first by the
flux lines of a magnetic field.
Mutual inductance
The principle that a change of current in one circuit can induce
electromotive force in a neighboring circuit, equal to the ratio of the
electromotive force in a circuit to the corresponding change of
current in a neighboring circuit.
em = - rate of change of flux linkage from coil 1 to coil 2
Here M is constant .
In general ;
em =
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,
= flux
solenoid
A solenoid is a type of electromagnet when the purpose is to generate a
Solenoid
controlled magnetic field. If the purpose of the solenoid is instead to
impede changes in the electric current, a solenoid can be more
specifically classified as an inductor rather than an electromagnet.
Self inductance of solenoid :
N = number of turns
I = current in the solenoid
In case of ideal solenoid:
Length >> diameter
Energy
inducor
in
Energy stored in an inductor
This energy is actually stored in the magnetic field generated by the
current flowing through the inductor.
Energy (W) is given by:
Growth
and
decay of current
inside I-R circuit
Growth of current in an L – R circuit
Growth is given by equation :
Imax = E/R
 L behaves as open circuit at t = 0 [if I = 0]
 L behaves as short circuit at t =
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Decay of current in I- r circuit
I = I0
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