The electron moves in a circular path of radius
under the influence of the inward force

Now we add magnetic field in the direction out of the page. The inward force
increases
to

so
either
or
must change. previously we aserted that
changes, and
thus

so

We
are to show that the induced electric field produces exactly this change in
With positive direction around the circle defined to be clockwise, the induced
electric field is given
by

So

and
the force tangent to the electron's path that changes its speed
is

Integrating,
we
get

as
required.