Magnitude and direction of current

AI Thread Summary
To keep a conducting bar stationary on a frictionless inclined plane in a uniform vertical magnetic field, the current must be adjusted to balance the gravitational force acting on the bar. The relevant equation is F = I(l × B), where the direction of the magnetic force must be carefully considered. The component of gravitational force acting down the slope is mg sin θ, which does not align with the vertical direction. The discussion emphasizes correcting the use of unit vectors in the force equations. Properly balancing these forces will ensure the bar remains stationary.
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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.
 
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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.
 
Thank you for the answer.How silly of me to use that unit vector k.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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