A long straight wire carries a current of 50.0 A. An...

A long straight wire carries a current of $50.0$ A. An electron, traveling at $1.0 \times 10^{7} \mathrm{~m} / \mathrm{s}$, is $5.0 \mathrm{~cm}$ from the wire. What force (magnitude and direction) acts on the electron if the electron's velocity is directed toward the wire?

Key Concepts

Magnetic Field from a Current-Carrying Wire

This concept involves understanding that a long straight wire carrying a steady current produces a magnetic field whose magnitude at a distance r from the wire is given by B = ??I/(2?r). The field lines form concentric circles around the wire, and the magnitude decreases with increasing distance. This principle is a direct result of Ampère's law and is foundational in electromagnetism.

Lorentz Force

The Lorentz force describes the force experienced by a charged particle when it moves through a magnetic field. Its magnitude is given by F = q(v × B), meaning the force is perpendicular to both the velocity of the particle and the magnetic field. The sign of the charge determines the direction of the force, which is critical when analyzing the behavior of electrons and other charged particles in magnetic fields.

Right-Hand Rule

The right-hand rule is a practical tool used to determine the direction of the magnetic field created by a current-carrying conductor as well as the direction of the force on a moving charge in a magnetic field. By orienting the thumb in the direction of the conventional current, the curled fingers indicate the direction of the magnetic field lines. A similar approach is used to find the direction of the Lorentz force, ensuring correct vector directions in electromagnetic problems.

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