Question

A wire that is bent at its midpoint such that one half iof its length (0.250 m) lies along the +z axis and the other half (also 0.250 m in length, of course) lies along the line y=2x in the xy plane. A 20.0 A current passes along the wire down the z axis and then out the half that lies in the xy plane. The entire wire is in a constant magnetic field of 0.318 ? ?.̂ Find the magnitude of the net force acting on the entire wire.

need all work show also please

Answer 1

Magnetic force on the wire is given by:

When the current is along negative z axis, from cross-product rule, the force will be along negative y direction (since the magnetic field is along positive x direction).

Its magnitude will be: F = 0.250(20.0)(0.318) = 1.59 N

When the wire is in the xy plane, the angle the wire makes with the x axis is:

since the x component of this current will be parallel to the magnetic field, the force for this will be zero. However, for the current component along the positive y direction, from cross-product rule, the force will be along negative z direction with magnitude:

so, the net force on the wire will be: