Two long straight aluminum wires, each of diameter 0.50 mm , carry the same current but in oppos

step 1 There are three forces acting on each wire. It's a weight acting in the downward direction, the

Two long straight aluminum wires, each of diameter 0.50 mm ,...

Two long straight aluminum wires, each of diameter 0.50 $\mathrm{mm}$ , carry the same current but in opposite directions. They are suspended by 0.50 -m-long strings as shown in Fig. $20-71$ . If the suspension strings make an angle of $3.0^{\circ}$ with the vertical, what is the current in the wires?

Key Concepts

Magnetic Force Between Parallel Currents

When two long, parallel current-carrying wires carry currents, they exert magnetic forces on one another. This force per unit length is given by the expression F/L = (?? I? I?)/(2?d), where ?? is the permeability of free space, I? and I? are the currents in the wires, and d is the separation between the wires. This concept arises from Ampère’s Law and the Biot–Savart Law, and it explains how neighboring currents attract or repel depending on their direction.

Magnetic Field of a Long Straight Conductor

A long straight conductor carrying an electric current produces a magnetic field around it. This magnetic field at a distance r from the wire has a magnitude given by B = (??I)/(2?r), and its direction is determined by the right-hand rule. Understanding this relationship is crucial when calculating the force that one current-carrying wire exerts on another.

Force Equilibrium in a Suspended System

In the context of wires suspended by strings, mechanical equilibrium is maintained when the horizontal magnetic force between the wires is balanced by the horizontal component of the tension in the supporting strings. Analyzing the force components involves resolving the tension into vertical and horizontal parts and applying Newton’s first law, where the horizontal magnetic force equals the weight times the tangent of the suspension angle.

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