Magnetic Interaction: parallel rods, cross bar free to slide

[MaryCate22]

Homework Statement

Two horizontal parallel conducting rods are connected such that a conducting crossbar free to slide along them has a constant current I running through it (Figure 1) . The rods are separated by a distance ℓ and are in an external uniform magnetic field of magnitude B directed out of the screen. The crossbar has a length ℓ and mass m.

Part A: In which direction does the crossbar move?
Part B: If there is a coefficient of static friction μs between rods and crossbar, what is the minimum current I₀ necessary for the crossbar to move? For the length ℓ of the bar use the notation L.
Express your answer in terms of some or all of the variables L, B, m, μs, and the acceleration due to gravity g.

Homework Equations

F=ILsin(theta)

The Attempt at a Solution

For Part A I think it moves to the right. Got this using the right hand rule.
I'm not sure how to go about Part B.

F=I₀LB

I don't know how to incorporate the coeff of friction in this. What can I set it equal to?

 

[NascentOxygen]

The force on the rod due to interaction of the magnetic fields must > the force due to friction.