Magnetic force on a current carrying wire

[pantheid]

Hi, I am slightly confused by the formula for finding the force on a current carrying wire. It is given as F=BIL where F is force, B is the strength of the magnetic field and L is the length of the wire being acted upon. What I don't understand is why this formula doesn't factor in the distance between the magnet and the wire itself.

 

[stevenb]

Hi, I am slightly confused by the formula for finding the force on a current carrying wire. It is given as F=BIL where F is force, B is the strength of the magnetic field and L is the length of the wire being acted upon. What I don't understand is why this formula doesn't factor in the distance between the magnet and the wire itself.

The magnetic field B is taken to be the field present at the wire itself. Any position dependence of B must be known in order to know the field at the wire. So, yes a far aways magnet will have less force on the wire, but it will also present less magnetic field to the wire. You would not want to use the value of B near the magnet in the calculation of force on a wire a long distance away.

Note that this formula is a simplification that assumes the magnetic field is uniform over the entire length of the wire, which is not likely to be true for a real magnet and a wire of any appreciable length.

 

[NascentOxygen]

The usual arrangement for demonstrating this involves using a pair of bar magnets (using the gap between a N and opposing S pole), or else a horseshoe magnet, and this arrangement makes the field in that region approximately uniform.