A long straight wire carries 2.5 A along the +x -axis. Find...

A long straight wire carries 2.5 A along the $+x$ -axis. Find the magnitude and direction of the magnetic field at (a) a point $15 \mathrm{~cm}$ away on the $+y$ -axis and (b) a point $15 \mathrm{~cm}$ away on the $-y$ -axis.

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Key Concepts

Magnetic Field of a Long Straight Conductor

This concept involves calculating the magnetic field produced by a long, straight current-carrying wire. The magnetic field's magnitude is given by the formula B = (??I) / (2?r), where ?? is the permeability of free space, I is the current, and r is the perpendicular distance from the wire. This formula is derived from Ampère's Law applied to the symmetry of the configuration.

Ampère’s Law

Ampère’s Law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. In scenarios involving a long straight wire, the symmetry simplifies the application of this law, helping derive the expression for the magnetic field at a given distance from the wire.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field around a current-carrying conductor. By pointing the thumb of the right hand in the direction of the conventional current, the curled fingers indicate the direction in which the magnetic field circles the wire, thereby providing the directional component needed to completely describe the magnetic field at any point.

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