Answer 1:
What is happening is that a changing magnetic
field produces an electric field  i.e. a voltage.
Increasing the rate of change in the magnetic
field increases this voltage. A conductor, located
across an electric field, will pass a current
equal to the strength of the voltage divided by
the resistance of the conductor. Thus, with a
given voltage, a better conductor (like a
superconductor) will pass more current than a less
good conductor, just as increasing the voltage
will also increase the current.

Answer 2:
Your question is very interesting.If we
mathematically analyze it, we have to make clear
that the answer is different when the voltage
arising from a changing magnetic field is held
constant, than when it is a varying one (as when
you move the magnet back and forth in a simple
harmonic motion). Here you also have to consider
that the resistance R in a superconductor is zero,
R=0 (a characteristic of conducting metals when
they behave as a superconductors), then all the
results will depend on the voltage, the inductance
of the wires and time.
In the first case,
when the voltage is constant (there is not a
change of magnetic field), the current in the
superconductor increases without a boundary (which
is unrealistic, since the magnetic field would
also have to increase without boundary (Faradays
law)). This situation does not happen with a
copper conductor, which has a current limited by
the voltage and the value of the resistance.
In the case when the voltage is a varying
one, the current in the superconductor will
increase more than the current in the copper coil,
but it will be directly limited by the magnitude
of the voltage, and inversely limited by the
inductive effect and the frequency at which the
voltage signal moves. The magnitude of the
current will be given by:
Voltage/(inductance x 2pi x
frequency of voltage signal)
Then,
replacing the copper coil with a superconductor
Type2 coil, will make a higher current, but will
still be limited by the rate of changing magnetic
field.
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