Energy stored in a magnetic field

Consider a circuit consisting of a voltage supply,  switch,  resistor  and  a  coil  of  N turns wound on a toroid of length l, all in series.

With the switch open, no current flows inthe coil and therefore there is no flux produced in the core of the coil.

At t=0, the switch is closed and the current builds up with time. It is not instantaneous,because the coil produces a back emf that limits the rate of rise of current

where v = the time dependent back emf created by the coil. The instantaneous power being delivered
by the supply at time t is

v_s .i=i² R+v.i