A particle of charge q=7.2 μC is moving at an angle of 25^∘...

A particle of charge $q=7.2 \mu \mathrm{C}$ is moving at an angle of $25^{\circ}$ with respect to the $x$ axis with a speed of 250 $\mathrm{m} / \mathrm{s}$. A constant magnetic field of magnitude $0.55 \mathrm{T}$ is parallel to the $+x$ direction. Find the magnitude of the magnetic force on the particle.

Key Concepts

Unit Conversion

Consistent use of SI units is fundamental in physics calculations to ensure accuracy. When dealing with physical quantities like charge, converting microcoulombs to coulombs is necessary before applying the formulas. This conversion helps in avoiding errors and in achieving the correct magnitude for the computed force.

Trigonometric Decomposition

Trigonometric decomposition involves breaking a vector into its components, particularly when it is not aligned perfectly with another reference direction, such as a magnetic field. In the problem, the sine of the angle between the particle's velocity and the magnetic field is used to determine the effective component of the velocity that interacts with the magnetic field. This concept is key in calculating forces when vectors are oriented at an angle to each other.

Lorentz Force Law

The Lorentz force law describes the force that a charged particle experiences when moving through a magnetic field. This force is given by the equation F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field. It is essential in electromagnetism because it explains how charges are influenced by magnetic fields, resulting in forces that are perpendicular to both the velocity of the particle and the magnetic field direction.

Vector Cross Product

The cross product of two vectors provides a way to calculate the magnitude and direction of the resultant vector that is perpendicular to the plane containing the original vectors. In the context of the magnetic force, the magnitude of the force is given by |q||v||B| sin(?), where ? is the angle between the velocity and the magnetic field. This concept is crucial because it shows that only the component of the velocity perpendicular to the magnetic field contributes to the force.

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