Magnetic coupled circuit
You can technically write KVL for the second loop and find that only \$I_2=0\$ satisfies it. I suppose the purpose of this task is to train you in application of the dot rule (which is simple: mutual inductance e.m.f. has the same sign as self inductance e.m.f. when both the loop current and the coupled current are flowing in or out of dotted ends; the signs are opposite otherwise); you have to apply it 4 times for your second loop.
You did it well with the first loop.
Physically you have a transformer with two secondary windings, connected in opposite directions. Voltage from the one winding cancels voltage from the other, so the second loop has no current.