The magnetic field inside the solenoid is parallel to its axis. If the plane of the loop contains the axis of the solenoid, the angle between the area vector of a circular loop and the magnetic field will be zero.

The formula used: The flux through the circular loop is given by

Where is the electric flux

B is the magnetic field due to the solenoid

A is the Area of the circular loop

is the Angle between magnetic field and area vector

=constant

Then the induced emf is given by

Because BA is constant

The induced emf does not depend on the varying current through the solenoid. The induced emf will be zero for a constant flux through the loop. So no current will be induced in the loop.