Magnitude and direction of current

[Steenrod]

Homework Statement

A conducting bar of length l is placed on a frictionless plane tilted at an angle θ from the horizontal.A uniform magnetic field is applied to the vertical direction.To prevent the bar from sliding down, a voltage source is connected to the ends of the bar with current flowing through.Determine the magnitude and direction of the current such that the bar will remain stationary.

Homework Equations

I think F=I(l×B) is relevant here.As besides B=B k-cap. But I am not sure I am on the right track. Could anyone please tell me how to proceed?I was trying to balance force F by F=mg sin θ (k-cap)= I(l×B). But it seems to make no sense.

 

[TSny]

You're on the right track. You'll need to consider the direction of the magnetic force when deciding how to balance the forces. Note that the component of the gravitational force mgsinθ does not point in the z direction. So, you don't want the "k-cap" in the expression for this component of force.

 

[Steenrod]

Thank you for the answer.How silly of me to use that unit vector k.