let us discuss about magnetic moment of a
rotating charged ring. say we are given with
a circular ring. which is of radius r, and
it is uniformly charged.
with a positive charge q. now if the ring
is rotated at an angular speed omega. we can
see that.
due to a continuous rotating charge there
will be an equivalent current.
and here we can directly write that equivalent
current.
due to circulation of charge.
is.
this equivalent current we can directly write
as.
charge multiplied by revolution frequency
to find out the amount of charge flowing per
unit time. and here it can be given as charge
multiplied by omega upon 2 pie.
so the equivalent current is q omega by 2
pie. and if we wish to find out the magnetic
moment.
of this current.
or this equivalent current.
the magnetic moment can directly be given
as, m. which is given by.
current multiplied by the enclosed area that
is i-a so here we can write current is.
q omega by 2 pie multiplied by the enclosed
area pie r square.
here pie gets cancelled out and the magnetic
moment is half q omega r square.
in the direction we can see as current is
flowing in clockwise direction the magnetic
moment by righthand thumb rule will be given
as. in inward direction so this m vector is
into the plane of the surface.
that is the direction of this magnetic moment
vector. for any other charged body in the
similar manner we can find out first the equivalent
current due to the circulation of charge or
elemental charge is in case of.
extended bodies. and finally we can calculate
the magnetic moment corresponding to the.
rotating equivalent current due to, the rotation
of object.
