Suppose a loop of conductor is intitially carrying no current and is
placed in a changing magnetic field for time T, and the induced
current is allowed to go back to zero. If this is repeated with the
magnetic field changing in the same way, will the induced I circulate
clockwise 50% of the time, anti-clockwise 50%?
The current will not go back to zero unless the magnetic field
enclosed by the loop stops changing. The current will always be
proportional to the rate of change of the enclosed magnetic flux. A
change in flux is implied by moving the loop into or out of a static
magnetic field, or by changing the area of the loop, or by the
intensity of the magnetic field changing. An increase in N-S magnetic
flux is equivalent to a decrease in S-N magnetic flux, etc. The
current's direction will be such that the current's induced magnetic
field will tend to maintain the total flux through the loop constant.
So, the direct answer to your question is, the magnetic field must
stop changing for the current to fall to zero. If the field then
starts increasing from its steady level in the same direction, the
current will resume in the same direction.
If the magnetic field was increasing, and then was allowed to decrease
to zero, the current would reverse, then fall to zero. Then,
increasing the magnetic field in the original direction would cause
the current to rise in the original direction.