A long straight rent of 50.0 A. An electron, traveling at 1.0 ×10^7 m / s, is 5.0 cm from the wi

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A long straight rent of 50.0 A. An electron, traveling at...

A long straight rent 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

Vector Cross Product and Right-Hand Rule

The direction of the force experienced by a moving charge in a magnetic field is determined by the cross product (v × B). The right-hand rule is used to find the direction of this cross product, where the fingers point in the direction of the velocity and curl toward the magnetic field, giving the direction of the force for a positive charge. For a negative charge, such as an electron, the force is in the opposite direction to that indicated by the right-hand rule.

Magnetic Field around a Current-Carrying Wire

A long straight wire carrying electric current produces a magnetic field that loops around the wire. The magnitude of this field at a distance r from the wire is given by B = (??I)/(2?r), where ?? is the magnetic constant and I is the current. This concept is fundamental in understanding how currents generate magnetic fields, as described by Ampère’s law.

Lorentz Force on a Moving Charge

A charged particle moving in a magnetic field experiences a force known as the Lorentz force, which is mathematically given by F = q(v × B). Here, q is the charge of the particle, v is its velocity, and B is the magnetic field. This force is perpendicular to both the velocity and the magnetic field, and its magnitude depends on the speed of the particle, the strength of the field, and the angle between them.

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