Question
One long straight wire is to be held directly above another by repulsion between their currents. The lower wire carries 100 A and the wire 7.50 cm above it is 10-gauge (2.588 mm diameter) copper wire. (a) What current must flow in the upper wire, neglecting the Earth’s field? (b) What is the smallest current if the Earth’s $3.00\times 10^{-5}\textrm{ T}$ field is parallel to the ground and is not neglected? (c) Is the supported wire in a stable or unstable equilibrium if displaced vertically? If displaced horizontally?
1. $1.70\times 10^{3}\textrm{ A}$
2. $1.53\times 10^{3}\textrm{ A}$
3. With vertical displacement the equilibrium is stable since forces will adjust such that a net force accelerates the wire back to its original position. When moving up, repulsion will reduce whereas gravity will not change significantly, in which case there will be a net force due to gravity back down. When moving down, repulsion will increase resulting in a net force back up. With horizontal displacement the equilibrium is unstable since forces will adjust to cause further movement horizontally away form the original position. The wire repulsion will be directly away from the bottom wire, but there will now be a horizontal component pushing the top wire further to the side.

# OpenStax College Physics, Chapter 22, Problem 84 (Problems & Exercises)

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