A horizontal wire carries a large current. A second wire carrying a current in the same direction is suspended below it.Can the current in the upper wire hold the lower wire in suspension against gravity?

http://physics.bu.edu/~duffy/semester2/c14_forcewires.html

To determine whether the current in the upper wire can hold the lower wire in suspension against gravity, we need to consider the magnetic forces between the wires.

The magnetic field produced by the current flowing in the upper wire will generate a magnetic field around it. The magnetic field lines form concentric circles around the wire, with their direction determined by the right-hand rule.

When the current-carrying upper wire is positioned above the lower wire, the magnetic field lines generated by the upper wire will intersect with the lower wire. According to Ampere's Law, the magnetic field lines will exert a force on the lower wire.

To calculate the force exerted on the lower wire, we can use the formula for the magnetic force between two parallel current-carrying wires:

F = (μ₀ * I₁ * I₂ * ℓ) / (2π * d)

Where:
F is the force between the two wires,
μ₀ is the permeability of free space (a constant),
I₁ and I₂ are the currents in the first and second wires respectively,
ℓ is the length of the wire segments in the interaction, and
d is the distance between the wires.

If we assume that the current in the upper wire is sufficiently large and the distance between the wires is small, the force calculated using the formula above can potentially counteract the gravitational force pulling the lower wire down. However, the feasibility of such a setup depends on various factors like the current magnitude, wire length, wire materials, and the distance between the wires.

In conclusion, the current in the upper wire has the potential to hold the lower wire in suspension against gravity, provided certain conditions are met. The exact calculations and practical considerations would need to be analyzed to determine the feasibility.