Why does magnetic force equal to weight guarantee vertical lift?

[Bashyboy]

Homework Statement

A wire having a mass per unit length of 0.560 g/cm carries a 1.90-A current horizontally to the south.

(a) What is the direction of the minimum magnetic field needed to lift this wire vertically upward?

(b) What is the magnitude of the minimum magnetic field needed to lift this wire vertically upward?

Homework Equations

The Attempt at a Solution

What I am having difficulty understanding is, how does this condition $F_B = F_{mg}$ guarantee that the magnetic force $F_B$ will cause the the wire to raise vertically? If I hold a can such that the force I exert on it from the palm of my hand $F_h$ is equal and opposite to the gravitational force on it, it doesn't necessarily have to move upwards. Could someone explain this to me?

 

[djh101]

Replace = with > and, yes, the wire will raise vertically. If the only two forces acting on the can are your hand and gravity, the can will move upward if the force of your hand (upward) is greater than the force of gravity. Always. Because F = ma (and there is no reason for m not to be constant).

 

[Bashyboy]

That's what I figured. Thank you very much.