How Does Doubling the Current Affect the Compass Needle's Deflection Angle?

[IIK*JII]

Homework Statement

A conducting wire runs directly over a horizontal compass in the north-south direction. When a current of magnitude I passes through the wire, the compass needle swings 20° to the west and stays in that position.

When a current of 2I passes through the wire, the compass needle swings α° to the west and stops. What condition does α fulfill?

Homework Equations

I used M(couple moment) = BIANcosθ　

The Attempt at a Solution

　　 I am not sure that at does the moment between the 1st event (when I passes) and the 2nd event (2I passes) equal?
I guess it is not because I my answer is wrong when I assume like this... But what is the relationship between 1st and 2nd event for solving this problem...

Help is appreciate..
Thanks in advance :)

 

[TSny]

The compass needle points in the direction of the net B field which is the vector sum of the field of the Earth and the field of the wire.

Think about the direction of these two fields and draw a sketch showing their vector sum. Make a similar sketch for the case where the current is doubled. Identify the angle of 20^o in the first sketch and the angle α in the second. Use an appropriate trig function to relate the two angles.