Magnetic Force on A Curved Current Carrying Wire

[astralboy15]

Ok, just a quick question. I'm working through a problem in my physics book and I am asked to find the magnetic force on a current carrying wire that runs along the equator of a sphere. So the wire is not straight, but curves along with the sphere, off the surface of it (not levitating).

My book also mentions that the magnetic force on a curved current carrying wire is the same as the magnetic force on a straight wire connecting the either end with the same current.

My question is this:

Am I to assume that if I only have the CURVED portion of wire (there is nothing connecting either end) that I could simply find the magnetic force of a straight wire of the same length and they would have the same magnetic force acting on them?

 

[vela]

It depends on the magnetic field, which you haven't told us anything about. The claim the book makes about the forces being equal probably relies on assumptions about the magnetic field, like it being uniform and the wires lying in a plane perpendicular to the field.

 

[astralboy15]

Ok, true, my bad - forgot to put that bit in. The magnetic field is uniform. It is also horizontal.
Think of the curved portion of the wire (elevated, not levitated, along the sphere) then the magnetic field running uniformly beneath it in a horizontal plane. In other words, look at this, +, and imagine this being a cartesian coordinate system: the magnetic force is running from -y to y (in a horizontal plane), the wire curves along the sphere with current running -x to x.

hope this helps. thanks guys!