·Two high-current transmission lines carry currents of 25 A and 75 A in the same direction and a

step 1 We have a following situation, two wires, the current 75 ampires and 25 ampere respectively. The

·Two high-current transmission lines carry currents of 25 A...

$\cdot$ Two high-current transmission lines carry currents of 25 $\mathrm{A}$ and 75 $\mathrm{A}$ in the same direction and are suspended parallel to each other 35 $\mathrm{cm}$ apart. If the vertical posts supporting these wires divide the lines into straight 15 $\mathrm{m}$ segments, what magnetic force does each segment exert on the other? Is this force attractive or repulsive?

Key Concepts

Magnetic Field of a Current-Carrying Conductor

A current flowing through a conductor generates a magnetic field that encircles it. The magnitude of this magnetic field at a distance is given by the formula B = (??I)/(2?r), where ?? is the magnetic permeability of free space, I is the current, and r is the radial distance from the conductor. This concept is fundamental in electromagnetism and is used to analyze interactions between current-carrying wires.

Force between Parallel Currents

Two parallel conductors carrying currents exert a magnetic force on each other due to the interaction of one conductor’s magnetic field with the current in the other. The force per unit length between them is given by F/L = (??I?I?)/(2?d), where I? and I? are the currents and d is the separation distance. This force is attractive if the currents flow in the same direction and repulsive if they flow in opposite directions, playing a key role in the analysis of magnetic interactions.

Right-Hand Rule in Magnetic Interactions

The right-hand rule is a mnemonic used to determine the direction of the magnetic field around a current-carrying conductor and the direction of the force experienced by a conductor in a magnetic field. By pointing the thumb in the direction of the conventional current and curling the fingers, one can visualize the circular magnetic field lines surrounding the wire. This concept is essential for understanding the spatial orientation of forces in electromagnetic problems.

Magnetic Permeability of Free Space (??)

The magnetic permeability of free space, denoted by ??, is a physical constant that characterizes the magnetic properties of a vacuum. It appears in the equations governing the magnetic field generated by currents and the force interactions between conductors. Understanding ?? is important as it directly influences the strength of the magnetic field and the resulting force between current-carrying wires.

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