Two massless parallel current carrying wires are supported...

Two massless parallel current carrying wires are supported by strings as shown in the diagram. If each of the wires is $1 \mathrm{~m}$ long and carries a current of $50 \mathrm{~mA}$, and the supporting strings are $85 \mathrm{~cm}$ long, calculate the force acting on each of the wires when the angle between the strings is $60^{\circ}$.

Key Concepts

Vector Decomposition and Trigonometry

The analysis of forces often requires breaking them down into their components using vector decomposition. Trigonometric functions, such as sine and cosine, are applied to resolve forces along different axes, especially when forces act at angles. This concept is vital when real-world forces are not aligned with the coordinate axes, allowing for accurate analysis and calculation of resultant forces.

Equilibrium of Forces

In mechanical systems, for an object to remain stationary, the sum of the forces acting on it must be zero. This principle of equilibrium involves balancing different forces, such as magnetic forces and tension in supporting strings. Understanding force equilibrium is essential for analyzing systems where multiple forces interact to maintain a stable configuration.

Magnetic Field of a Current-Carrying Conductor

A current-carrying conductor produces a magnetic field in its surroundings, the strength and direction of which can be determined using the Biot–Savart law. This concept is fundamental in electromagnetism and explains how moving charges generate magnetic fields that influence other nearby currents or magnetic materials.

Force between Parallel Currents

When two parallel conductors carry electric currents, they exert forces on each other due to their magnetic fields. This phenomenon is described by Ampère’s force law, which shows that the force per unit length between the conductors is proportional to the product of the currents and inversely proportional to the distance between them. This key concept is crucial for understanding interactions in electrical circuits and devices.

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