In Fig. 29-57, four long straight wires are perpendicular to...

In Fig. $29-57,$ four long straight wires are perpendicular to the page, and their cross sections form a square of edge length $a=8.50 \mathrm{cm} .$ Each wire carries 15.0 $\mathrm{A}$ , and all the currents are out of the page. In unit-vector notation, what is the net magnetic force per meter of wire length on wire 1?

In Fig. $29-57,$ four long straight wires are perpendicular to the page, and their cross sections form a square of edge length
$a=8.50 \mathrm{cm} .$ Each wire carries 15.0 $\mathrm{A}$ , and all the currents are out of
the page. In unit-vector notation, what is the net magnetic force per
meter of wire length on wire 1?

Key Concepts

Magnetic Force on a Current-Carrying Wire

This concept explains that a current-carrying wire placed in an external magnetic field experiences a force described by the equation F = I L × B, where I is the current, L is a vector in the direction of the current with a length equal to the segment of the wire considered, and B is the magnetic field vector. The direction of the force is determined by the right-hand rule, and this principle is crucial for determining the interactions between wires carrying currents.

Superposition Principle in Electromagnetism

The superposition principle states that when multiple magnetic fields are present, the net magnetic field at any point is the vector sum of the individual magnetic fields produced by each current-carrying wire. This principle allows one to calculate the total magnetic environment affecting a specific wire by considering the contributions from all other wires in the system.

Magnetic Field Due to a Long Straight Wire

This concept involves understanding that a long straight wire carrying an electric current produces a magnetic field that circulates around the wire. The magnitude of the magnetic field at a perpendicular distance from the wire is given by B = (?? I)/(2?r), where ?? is the permeability of free space, I is the current, and r is the distance from the wire. This result is derived using Ampère's Law and is fundamental in analyzing the magnetic interactions between current-carrying wires.

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