The three wires shown in FIGURE 22-53 are long and straight,...

The three wires shown in FIGURE $22-53$ are long and straight, and they each carry a current of the same magnitude, I. The currents in wires 1 and 3 are out of the page; the current in wire 2 is into the page. What is the direction of the magnetic force experienced by wire 3$?$

Key Concepts

Lorentz Force on a Current-Carrying Conductor

When a current-carrying wire is placed in an external magnetic field, it experiences a force described by the Lorentz force law, F = I L × B. This vector cross-product implies that the force is perpendicular to both the current direction and the applied magnetic field, with the exact direction given by another application of the right-hand rule. This concept is fundamental in understanding the interaction between magnetic fields and moving charges in conductors.

Superposition Principle for Magnetic Fields

In scenarios where multiple current-carrying wires create overlapping magnetic fields, the net magnetic field at any point is the vector sum of the individual magnetic fields produced by each wire. This principle is crucial for analyzing complex magnetic environments, allowing for the calculation of the resultant field and, consequently, the resultant forces experienced by current-carrying elements within that field.

Magnetic Field due to a Current-Carrying Conductor

A long, straight current-carrying wire produces a magnetic field whose magnitude decreases with distance from the wire, following the relationship B = ??I/(2?r). The direction of this magnetic field is determined by the orientation of the current and is given by a circular pattern around the wire. This concept forms the basis for analyzing the magnetic environment created by current flows in conductors.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field around a current-carrying conductor or the force on a conductor in a magnetic field. For example, if you point the thumb of your right hand in the direction of the current, the curl of your fingers will indicate the direction of the magnetic field lines encircling the wire. This tool is essential for visualizing and predicting the behavior of magnetic fields in various configurations.

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