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You should think twice before letting students observe the system
as a lab exercise, because of the possibility of blowing the front
end off the oscilloscope. There are lots of ways of protecting
against this, but I don't at the moment see how to prevent students
from bypassing the protection
You can't have it both ways.
If you want to make the magnetic field collapse faster, you don't
want a capacitor in there, since it provides a path for the current
to keep flowing. And making the field collapse faster provably
means having a higher voltage across the open points, which is the
opposite of what you want if you are trying to protect the points.
It would be closer to the truth to say that the capacitor protects
the points by allowing the magnetic field to collapse more slowly
... but that is an overly simplistic view of the situation. It is
better to analyze the circuit as a whole. The capacitor doesn't do
only one thing; there is a choreographed interplay between the R,
the L, the C, the battery, and the switch.