∙In a 1.25 T magnetic field directed vertically upward, a...

$\bullet$ In a 1.25 T magnetic field directed vertically upward, a particle having a charge of magnitude 8.50$\mu \mathrm{C}$ and initially moving northward at 4.75 $\mathrm{km} / \mathrm{s}$ is deflected toward the east. (a) What is the sign of the charge of this particle? Make a sketch to illustrate how you found your answer. (b) Find the magnetic force on the particle.

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Key Concepts

Lorentz Force

This concept refers to the force experienced by a charged particle moving in a magnetic field, mathematically expressed as F = q(v × B). It is fundamental to understanding how charged particles interact with magnetic fields, resulting in mutual perpendicular components from velocity and field directions.

Right-Hand Rule

The right-hand rule is a mnemonic for determining the direction of the force on a positively charged particle moving in a magnetic field. By pointing your fingers in the direction of the velocity and curling them toward the magnetic field, your thumb points in the direction of the force. For a negatively charged particle, the force is in the opposite direction, making this tool essential in deducing the particle's charge sign based on its deflection.

Magnetic Force Magnitude

The magnitude of the magnetic force is calculated using the formula F = |q|vB sin(?), which, for perpendicular motion (? = 90°), simplifies to F = |q|vB. This calculation is crucial for determining how strongly a particle is deflected in a magnetic field given its charge, speed, and the field's strength.

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