When I power up a DC coil the current increases rather slowly, so they
say. But is this true for the very, very first moment?
Are you talking about an ideal inductor? Real inductors are
extremely complicated. They're waveguides and radio antennas
and tuned circuits and inductors all in one. As soon as you
stop seeing them as ideal inductors, all the complexity comes
boiling out.
In the first few hundred picoseconds, waves of EM energy
are distributing a voltage-pattern through all the parts
of the inductor. Yet usually we can't turn the power
supply on in a matter of picoseconds. If it takes
hundreds of thousands of picoseconds for the voltage to
rise, then the energy-waves are too small to notice.
You do need a
current to get a counter EMF or????
You need an EMF to cause a current to begin rising.
Voltage is associated with e-fields and with the
push/pull upon electrons, so voltage causes current.
At atomic level, is the current equal everywhere in
the coil?
In ideal inductors, yes. In real inductors, no, not
in the first fractions of nanoseconds while waves are
bouncing around between different parts of the coil.
(Imagine sound waves bouncing around inside a long
plastic tube. Now imagine that you slowly raise the
speed of air flow in that tube without creating any
sound waves.)