Why does the left-hand rule work when Earth's field has a vertical component?

[jsmith613]

Homework Statement

At a certain point on the Earth's Surface the horizontal component of the Earth's magnetic field is 1.8 * 10^-5 T. A straight piece of wire 2m long and 1.5g lies on a horizontal wooden bench in an east-west direction. When a very large current flows momenterily in the wire it is JUST enough to cause the wire to lift off the bench surface.
State the direction of the current in the wire.

Homework Equations

NONE
Use left-hand rule

The Attempt at a Solution

What I don't understand is how we can use the left hand rule given the information. We don't know the direction of the magentic field (we were only given the horizontal componenet - i.e there is a vertical component too)

How is this done
(if it helps the answer is east)

 

[jsmith613]

does it have anything to do with the fact that the only magnetic field is horiztonal because the only force is up

 

[SammyS]

What do you know about the direction of Earth's magnetic field ?