Time varying fields
When any charge is at rest it produces electrostatic fields and when charge moves with
constant velocity, magnetic field is produces . Here electric and magnetic fields are independent
of each other in the time invariant fields.
Whenever any charge moves with an acceleration, it produces a time varying electric field
which then produces changing magnetic field. In the same manner a time varying magnetic field
produce a changing electric field. Hence oscillating electric field produces an oscillating magnetic
field and oscillating magnetic field produces oscillating electric field resulting in a wave like electric
and magnetic fields known as electromagnetic wave, which can transport energy over a very long
distances. Michael Faraday proposed the basis of electromagnetic field concept and gave postulates
for electromagnetic induction to relate time varying fields.
Electromagnetic Induction
Faraday in 1831, found that when there is a change in magnetic flux passing through any
circuit, an e.m.f. is generated in the circuit. A current flows in the circuit known as induced
current and emf as induced emf. This lasts till the change in flux exists. As soon as the change
stops, no emf or current is induced. This whole phenomenon is called electromagnetic induction.
Faraday's Laws of Electromagnetic Induction
1st Law : When number of magnetic lines of force attached to a closed circuit in changed,
an emf is induced in the coil which lasts up to the change of field lines.
2nd law : The magnitude of induced emf is directly proportional to the rate of change of
magnetic flux associated with the coil.
If is the change in magnetic flux in t time interval than the induced emf.
e =
t
as t 0
e = lim
t 0
e
t
d
volts
dt
if there are N turns in the coil, then the emf induced in the complete coil
e = N
d N
d
or
dt
dt
here N is called number of magnetic flux linkages. Its unit is weber turns.
3rd law : The direction of induced emf is such that it always opposes its cause of generation.
It is called Lenz's law.
e = N
Hence
d
dt
accordingly direction of induced emf can be found using flemming right hand rule.
Integral Forms
From Faraday's law of electromagnetic induction
d
dt
and magnetic flux through a closed surface is
B . ds
=
e =
s
...(i)
...(2)
If the electric field induced is E , then induced emf around the boundaries of closed surface
is
e =
E
. dl
...(3)
c
from (i), (ii) and (iii)
E . dl
c
d
= dt
B
. ds
s
B
E. dl t ds
c
s
or
...(4)
The equation (4) is known as the integral form of Faraday law of electromagnetic induction.
Differential form
From stoke's law we know that
E
. dl =
c
s
From (4) and (5)
E ds
s
E ds
B
= t ds
s
...(5)
or
or
B
E t ds = 0
s
B
E
t
...(6)
Equation (6) represents the differential form of Faraday's law of electromagnetic induction.
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