Two identical long straight conducting wires with a mass per...

Two identical long straight conducting wires with a mass per unit length of $25.0 \mathrm{~g} / \mathrm{m}$ are resting parallel to each other on a table. The wires are separated by $2.5 \mathrm{~mm}$ and are carrying currents in opposite directions. (a) If the coefficient of static friction between the wires and the table is $0.035$, what minimum current is necessary to make the wires start to move? (b) Do the wires move closer together or farther apart?

Key Concepts

Magnetic Field of a Long Straight Conductor

A long straight wire carrying a current generates a magnetic field that circles the wire according to the right-hand rule. The strength of the magnetic field at a given distance from the wire is inversely proportional to that distance. This fundamental aspect of magnetism is crucial for calculating the force experienced by another nearby current-carrying wire, as the field forms the basis for the magnetic interaction between conductors.

Static Friction and Force Equilibrium

Static friction is the force that prevents two surfaces in contact from sliding past each other until a threshold force is exceeded. In mechanical equilibrium, an applied force must overcome this static friction force to initiate movement. This principle is important for determining the conditions under which an additional force—in this case, the magnetic force between the wires—can overcome friction and set objects into motion.

Magnetic Force Between Parallel Currents

When two current-carrying conductors are placed near each other, each produces a magnetic field that influences the other. The interaction leads to either an attractive or repulsive force between the wires, depending on the direction of the currents. This force per unit length is quantified by Ampère’s force law, which relates the current magnitudes, the separation between the conductors, and the permeability of free space. This concept is central to understanding how electrical currents can generate mechanical forces.

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