dear students, let’s study a very important
concept of time varying magnetic fields, abbreviated
as t v m f. say we’re given with a magnetic
induction in which, a circular coil of enclosed
area ay is placed. so we can say that at any
instant specified magnetic flux is passing
through the coil. now say if this magnetic
field starts increasing with time. for which
we’re talking about time varying magnetic
field, we can say, if b changes, with time,
then we can say at any instant magnetic flux,
passing through the coil, also changes with
time, and if magnetic flux starts changing
with time, we can say it induces, an e m f
in coil. now in this situation we can see,
at any instant say if coil is having, n turns,
we can find out, the flux linked, with the
coil, which means we’re talking about total
flux linked with all the turns of coil, we
can write it as b, ay, n, as the flux passing
through the coil is b ay and there are n turns
so total flux linked will be b ay n. in this
situation we can write, the e m f induced
in this loop which is termed as, loop e m
f, which is written as mod of, d phi by d
t by faraday’s law. so in this situation
area and number of turns are constant so we
can write it as, ay d b by d t, multiplied
by the total number of turns. and this is
the total e m f in the loop, so it is written
as, distributed e m f, in loop. this is not
at any 2 points or we can say that this is
the potential difference across any 2 points
of the loop, here it is distributed, and the
direction of this loop e m f can be obtained
by lens law. as here if we consider b is increasing
with time in inward direction, then a current
is induced in the coil in such a way that,
it’ll oppose the downward inward, increment
in magnetic induction. so current will be
induced in anti clock wise manner so that
this current will, develop a magnetic induction
in outward direction, so as to oppose the
inward increment. so this is the direction
in which the loop current will be induced.
and to induce such a current if we talk about
this e m f it’ll be distributed at every
segment of the wire, or we can consider there
are small batteries, which are induced, or
small e m f which are induced throughout the
loop, in such a way that if several such e
m f’s are induced, all will cumulatively
induce a current in anti clock wise manner
in this loop. in this situation we can say,
if coil resistance, is r, induced current,
can be directly given as i is equal to, the
summation of all these e m f’s which is
the loop e m f divided by, the total resistance
of coil, which can be written as, ay n by
r multiplied by, d b by d t. so we must be
careful, whenever we’re required to find
the e m f induced, in a closed loop placed
in, time varying magnetic field it can be
given by, area multiplied by d b by d t, and
if there are some turns we can multiply it.
and we can also keep this note, that the direction
of, induced e m f or induced current, in time
varying magnetic field, is given by, this
can be directly obtained by lens law. as the
current is induced in such a way so as to
oppose, the increament or decreament in the
external field due to which the current or
e m f is induced.
