Physics
Physics
Problem
Three infinitely long thin wires, each carrying current in the same direction, are in the - plane of a gravity free space. The central wire is along the -axis while the other two are along . a. Find the locus of the points for which the magnetic field is zero. b. If the central wire is displaced along the -direction by a small amount and released, show that it will execute simple harmonic motion. If the linear density of the wires is , find the frequency of oscillation.Intuitive explanation
The key insight is that magnetic force between parallel currents follows a simple inverse-distance law, and you can use superposition to find the net force on any wire. Since all three currents flow the same direction, the outer wires attract the central one while repelling each other—the central wire experiences a net force of zero by symmetry, but the outer wires don't. Focus on how the force per unit length from one wire depends on distance, then add the contributions vectorially to find which wire (if any) experiences a net force and in what direction.
Intuitive explanation
The key insight is that magnetic force between parallel currents follows a simple inverse-distance law, and you can use superposition to find the net force on any wire. Since all three currents flow the same direction, the outer wires attract the central one while repelling each other—the central wire experiences a net force of zero by symmetry, but the outer wires don't. Focus on how the force per unit length from one wire depends on distance, then add the contributions vectorially to find which wire (if any) experiences a net force and in what direction.