A nonuniform magnetic field exerts a net force on a current loop of radius R. The figure shows a magnetic field that is diverging from the end of a bar magnet. The magnetic field B at the position of the current loop makes an angle θ with respect to the vertical, as the same magnitude at each point on the current loop. (I know that I need to solve in terms of R, I, B, and θ
The Attempt at a Solution
I fought the urge to use the force equation after substitution 2∏r for l. Instead I examined the force on one small segment and planned to integrate. The length would be in terms of arc length Δs. The I would be a constant. It seems that the problem indicates that the magnetic field B is constant (surely that is an assumption because the distance from the magnet was not indicated, right?) I also thought that the angle should be the only thing changing (I doubt this is a double integral problem). The subscript i indicates that this is for some segment i.
The first thing that jumps out at me is that we don't have the necessary Δθ, but we do have Δs. Δs=ΔθR, but this is for a different θ, right? So, here is where I got lost and thought that something was wrong.
Next I tried relating it with torque.
But here again we have a different θ value, correct?
I would very much appreciate some help. Thank you!