Two concentric current loops lie in the same plane. The outer loop has twice the diameter of the inner loop. The inner loop carries a 1.0 A current in a clockwise direction. What current, and which direction, should the outer loop carry such that the magnetic field in the center of the loops is zero

The current is 2 A and the current must flow counterclockwise

Explanation:

Like the magnetic field at center is zero, the magnetic field due to outer circle is equal the magnetic field due to inner circle, then the magnetic field due to inner circle is:

The magnetic field due to outer circle is:

B=B'

The current must flow counterclockwise.