divide 3x10 (let's say A,B,C).weigh A and B,
if balance, fake coil is in C. Weighing C and (A or B) will find fake coil is lighter or heavier.
Divide C into 2x5 and weigh them and find abnormal group(D).
Divide D to 2x2 and 1, weigh 2 and 2 -> if balance ,1 is fake. If not, in this case you already understand the abnormal side,reduce each coil from each side of beam scale and you will find out the fake coil ,may be it is in your hand or still on beam scale,
If no balance,weigh (A or B) and C will find fake coil group is lighter or heavier.Let's say fake coil is in A. Divide A (same as the bold sentence).
My Answer may be wrong.
Really sorry for my bad English and explanation.