Question

What magnetic field strength and direction will levitate the 2.0 g wire in

Short answer

The magnetic field has the magnitude of $0.13T$and points out of the paper

Step-by-step solution

Part 1 : Given Informaion

The magnetic force must be acting vertically upwards. since the field is perpendicular both to the wire and to the force, it must point in the direction perpendicular to the paper. we must have

$\stackrel{\rightharpoonup }{F}=\stackrel{\rightharpoonup }{Il}\times \stackrel{\rightharpoonup }{B}$.

Part 2 : Calculation

To get the desired direction, the field points out of the paper and magnitude of this force is

$F=ILB.$

It must balance the weight of the wire so

$ILB=mg,$

Yielding

$B=\frac{mg}{Il}.$

plugging in the numerical value we find

$B=0.13T$.