Two circular loops lie adjacent to each other on a tabletop. one is connected to a source that supplies an increasing current; the other is a simple closed ring. is the induced current in the ring in the same direction as that in the ring connected to the source, or opposite? what if the current in the first ring is decreasing?

Answer with Explanation:

The direction of the induced magnetic field is given by Lenz's Law which states that

"The direction of the induced current in a circuit is always in the direction such as to oppose the magnetic field that induced this current"

In the above case the direction of the current in the second loop will be  in same direction as that in the loop with increasing current so as to oppose the flux that is generated in it by the increasing current.

If the current in the first loop decreases the magnetic field this loop generates will also decrease with time. So the current in the second loop has to oppose this thus the current in the second loop will be in opposite direction to oppose this change.