let us study about the e m f induced in a
rotating coil in uniform magnetic field. here
we can see it is a rectangular coil, of enclosed
area ay and n turns, is placed in a uniform
magnetic induction b, and about the vertical
axis o o dash, it is rotating at an angular
speed omega. and say if at t equal to zero
it is, in a plane perpendicular to magnetic
field, we can write, the magnetic flux, linked
with coil, at t equal to zero is, this phi
can be written as b ay n, as total flux passing
through the coil is b ay and, through n turns
of coil the flux linked is b ay n. if we talk
about the flux after time t, and as the coil
is rotating at an angular speed omega, after
time t its area vector will rotate by an angle
omega t, so flux we can write as b ay n coz-theta
or coz omega t. right now the angle between
area vector and magnetic field vector is considered
to be zero, after time t area vector is at
an angle-theta to magnetic induction vector.
so flux will be b dot ay into n, that is b
ay coz-theta into n. and in this situation
if we calculate the e m f induced in coil,
as the flux is varying with time, so e m f
induced in coil we can write by faraday’s
law as mod of, d phi by d t. and on substituting
the values here we can say, e m f induced
will be equal to, b ay n, sine of omega t
multiplied by omega. and here b ay n omega
we can write as, e not sine omega t, where
we can write e not is, b ay n omega, that
can be written as peak e m f, induced in the
situation. and this e m f we can write as,
sinusoidal function or sinusoidal e m f, or
alternating current e m f induced. and this
is the basis of, making an alternating current
generator because, if we talk about the time
function of e m f, it is varying with sine
function like this, which is an alternating
current, oscillating between plus e not and
minus e not. this is the e m f induced whenever
a coil rotates in, uniform magnetic field
with peak value or amplitude of e m f given
as b ay n omega.
