Download faraday`s law in integral and point form

BABARIA INSTITUTE OF TECHNOLOGY
SUBJECT: ELECTROMAGNETICS
FACULTY GUIDE: MANSI RASTOGI
TOPIC: POINT AND LINE INTEGRAL FORM OF
MAXWELL’S EQUATION
MADE BY:TANUSHA SHARMA(130050111082)
PRABMEET SAINI(130050111062)
SUKAMAL NARANG(130050111519)
ANIRUDH VERMA(130050111094)
TIME-VARYING FIELD:
-
Moving loop in a time-varying field:A rectangular loop of metal wire, of width w, moving with
constant speed v, is entering a region of uniform B-field.
-The B-field is out of the page and is increasing at a constant
rate, where B0and  are positive constants.
At t = 0, the right edge of the loop is a distance x0into the field, as
shown. The motion of the loop and the changing of the B-field.
MOVING LOOP DIAGRAM:-
FARADAY’S LAW IN INTEGRAL AND POINT FORM:-
Electromagnetic induction was discovered independently
by Michael Faraday in 1831 and Joseph Henry in 1832.
 Faraday was the first to publish the results of his experiments.
 Based on his assessment of recently discovered properties of
electromagnets, he expected that when current started to flow
in one wire, a sort of wave would travel through the ring and
cause some electrical effect on the opposite side.
 He plugged one wire into a galvanometer, and watched it as he
connected the other wire to a battery.

Qualitative statement:•
The induced electromotive force in any closed circuit is equal
to the negative of the time rate of change of the magnetic flux
enclosed by the circuit.
•
Quantitative:Faraday's law of induction makes use of the magnetic
flux ΦB through a hypothetical surface Σ whose boundary is a
wire loop. Since the wire loop may be moving, we write Σ(t)
for the surface. The magnetic flux is defined by a surface
integral.
WHERE A IS AN ELEMENT OF SURFACE AREA OF THE MOVING
SURFACE Σ(T), B IS THE MAGNETIC FIELD (ALSO CALLED
"MAGNETIC FLUX DENSITY").
AND B·DA IS A VECTOR DOT PRODUCT (THE INFINITESIMAL
AMOUNT OF MAGNETIC FLUX THROUGH THE INFINITESIMAL AREA
ELEMENT DA).
Maxwell–Faraday equation:The Maxwell–Faraday equation is a generalisation of
Faraday's law that states that a time-varying
magnetic field is always accompanied by a spatiallyvarying, non-conservative electric field, and vice versa.
The Maxwell–Faraday equation is:-
AMPERE’S LAW IN INTEGRAL AND POINT FORM:Ampere's law relates magnetic fields to electric
currents that produce them. Ampère's law
determines the magnetic field associated with a
given current, or the current associated with a
given magnetic field, provided that the electric
field does not change over time.
 In its original form, Ampere's circuital law
relates a magnetic field to its electric current
source. The law can be written in two forms, the
"integral form" and the "differential form".


In terms of total current, which includes both free and bound
current, the line integral of the magnetic B-field around closed
curve C is proportional to the total current I passing through a
surface S.
where J is the total current density (in ampere per square metre,
Am−2).

In terms of free current, the line integral of the magnetic Hfield (in ampere per metre, Am−1) around closed curve C equals
the free current If, enc through a surface S:
where Jf is the free current density only. Furthermore
is the closed line integral around the closed curve C

denotes a 2d surface integral over S enclosed by C
is the vector dot product,

dl is an infinitesimal element (a differential) of the curve C.



Treating free charges separately from bound charges,
Ampere's equation including Maxwell's correction in
terms of the H-field is:-
where H is the magnetic H field, D is the electric
displacement field and Jf is the enclosed conduction
current or free current density. In differential form,
Maxwell’s Equation For Point Form:
Maxwell’s equation for line integral
RETARDED POTENTIAL
In electrodynamics, the retarded potentials
are the electromagnetic potentials for the
electromagnetic field generated by time-varying
electric current or charge distributions in the past.
RETARDED AND ADVANCED POTENTIALS FOR TIMEDEPENDENT FIELDS:

For time-dependent fields, the retarded potentials are
:-
where r is a point in space, t is time,