A constant flux travels through the secondary coil as a result of the battery's production of a constant current in the first coil. There is no induced voltage across the secondary coil if the flux through the secondary coil remains unchanged.
The value of induced current depends on the change in the flux which is produced due to the change in current in the primary coil, since the voltage is constant the current across the coil is also constant which results in 0 change in flux across the secondary coil which will result in no voltage.
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