A copper wire of length 26.0 cm is in a magnetic field of 0.390 T.
If it has a mass of 13.0 g, what is the minimum current through the wire
that would cause a magnetic force equal to its weight?

Question

A copper wire of length 26.0 cm is in a magnetic field of 0.390 T.
If it has a mass of 13.0 g, what is the minimum current through the wire
that would cause a magnetic force equal to its weight?

anonymous · Answer

The magnetic force on a current carrying wire is given as follows:$$F=ILBsin \left( \theta  \right)$$where F is force; I is current; L is the length of the wire; B is the magnetic field; and θ is the angle between the wire and the magnetic field.  Now, your problem doesn't specify and angle, so we can assume that θ=90°, which reduces the equation to:$$F=ILB$$
Now you nearly need to relate the weight of the wire to the magnetic force.

anonymous · Answer

...and that relationship is easy to define:$$F _{gravity}=F _{magnetic}$$$$mg=ILB$$where m is the mass of the wire; and g is the acceleration of gravity.