An electron moves with speed 2.0 ×10^5 m / s in a uniform magnetic field of 1.4 T, pointing sout

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An electron moves with speed 2.0 ×10^5 m / s in a uniform...

An electron moves with speed $2.0 \times 10^{5} \mathrm{m} / \mathrm{s}$ in a uniform magnetic field of $1.4 \mathrm{T},$ pointing south. At one instant, the electron experiences an upward magnetic force of $1.6 \times 10^{-14} \mathrm{N}$. In what direction is the electron moving at that instant? Be specific: give the angle(s) with respect to $\mathrm{N}, \mathrm{S}, \mathrm{E}, \mathrm{W},$ up, down. (If there is more than one possible answer, find all the possibilities.)

Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in electric and magnetic fields, given by the equation F = q(v × B). In the context of a magnetic field alone, the force is always perpendicular both to the velocity of the particle and the magnetic field, which means it does no work on the particle and only changes its direction of motion.

Vector Cross Product

The vector cross product is a mathematical operation that takes two vectors and produces a third vector that is perpendicular to both of the original vectors. In magnetic force problems, it is used to determine the direction of the magnetic component of the Lorentz force, since the force is obtained from the cross product of the velocity vector and the magnetic field vector.

Right-Hand Rule

The right-hand rule provides a guideline for determining the direction of the vector resulting from a cross product. When applying this rule to a positive charge, you point your fingers in the direction of the velocity, curl them toward the magnetic field, and your thumb then points in the direction of the force. For a negative charge such as an electron, the force is in the opposite direction to that indicated by the right-hand rule.

Charged Particle Motion in Magnetic Fields

Charged particle motion in magnetic fields is characterized by the force that acts perpendicular to the particle's velocity, causing the particle to undergo circular or helical motion. The analysis of such motion involves understanding how the components of velocity interact with the magnetic field to result in forces that continuously change the direction of the particle's trajectory without altering its speed.

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