Please help with this physics question if you can. Thank you very much?

Question

I've been trying for about 2 weeks. Cannot get the answer. Pleae help if you can. thanks

A long horizontal wire carries a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below. See the figure below. (a) Determine the magnitude and direction of the current in the lower wire. (b) Is the lower wire in stable equilibrium? (c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

Answer 1

The force per unit length between two current-carrying wires is

F / l = μ I1 I2 / 2 π d

and in your problem this force is equal and opposite to

F = mg

So you need the mass of the wire. You know the diameter and the density of copper, so figure mass per linear meter. Now the only unknown is the current in the second wire; solve for that.

Suspended below is unstable equilibrium; above is stable. One way to test this is to change the distance by some small amount Δd, solve for the force, and see if it tends to move the wire back towards the equibrium position. Another is just common sense. When below, if you pull the wire down, the attracting field becomes weaker, not stronger. When above, pulling the wire down repels the wire more strongly and returns it to equilibrium. And so on...