Surbhi Vishwak thanks her physics teacher Mr. Gyan Rao Dhote for allowing her to complete a school project on Faraday's law of electromagnetic induction. The document then provides the integral and differential forms of Faraday's law. The integral form states that the induced EMF is proportional to the rate of change of the magnetic flux through a circuit. The differential form results from applying Stoke's law and states that the curl of the electric field E is equal to the negative time derivative of the magnetic field B.

1. Submitted To :-
r.Gyan Rao Dhote SirSubmitted by
Surbhi Vishwak

2. I respect and thank Mr. gyanrao dhote sir our
physics teacher for giving me an opportunity
to do the project work on integral and
differential form of faraday’s law and
providing me all support and guidance which
made me complete the project on time. I am
extremely grateful to him for providing such a
nice support and guidance though he had
busy schedule managing the time.

3. ● Faraday’s law:- Faraday formulated the laws of
electromagnetic induction :-
1. Whenever there is a change in magnetic flux linked with
a conductor, an e.m.f. is induced. The induced e.m.f. lasts
so long as there is a change in magnetic flux linked with
the conductor. If the magnetic flux increases, the current is
in reverse direction and if the magnetic flux is decreases,
the current is induced in the same direction.
2. The magnitude of e.m.f. induced is directly proportional
to the rate of change of magnetic flux with the conductor.
So:-
the rate of change of magnetic flux = ᶲ2 -ᶲ1 / t
Integral form:-

4. e = -k( / t) --------(1)
where k is a constant.
If change in the magnetic flux is ∆t time.
Then we can write eq. (1) as :-
e = -∆ /∆t
if ∆t -> 0 then
e = -d / dt
so according to the faraday’s law –
e = -d / dt --------(2)
By definition, induced e.m.f. in a circuit is
equal to the work done per unit positive test
charge in moving the test charge through

5. that circuit, since work can be expressed as the line
integral of force and the force acting on a unit positive
charge is called the intensity of electric field E, hence
induced of e.m.f. e can be expressed as the line
integral of electric field E along that circuit :-
e = E . dl------(3)
in magnetic field B magnetic flux lined with a circuit
which encloses an area S is:-
= B.da
and due to change in magnetic flux , e.m.f. induced in
circuit e = E.dl
from eq. (3)

6. E.dl = -d/dt B.da------(4)
this eq. is known as integral form of faraday’s law.
Differential form-
● Stoke law:- According to stoke’s law, the line
integral of a vector field E along the boundary of a
closed curve C is equal to the surface integral of Curl
of that vector field when the surface integration is
done over a surface S enclosed by the boundary C.
E.dl = Curl E.da
Curl E.da = -d/ dt B.da
Hence from eq. (4)

7. or
(Curl E + dB/dt).da = 0
or
Curl E + dB/dt = 0
or
Curl E = -dB/dt
Now since magnetic field B depends on time as well
as on position, therefore dB/dt can be replaced by B/t
. Then
Curl E = - B / t
This eq. is knows as differential form of
faraday’s law.