A particle of charge q=-8.3 μC has a velocity of 600 m / s...

A particle of charge $q=-8.3 \mu \mathrm{C}$ has a velocity of $600 \mathrm{m} / \mathrm{s}$ that lies in the $x-y$ plane and makes an angle of $65^{\circ}$ with respect to the $x$ axis as shown in Figure $\mathrm{P} 20.22 .$ If there is a constant magnetic field of magnitude 1.5 T parallel to $+y,$ what are the magnitude and direction of the magnetic force on the particle?

Key Concepts

Vector Decomposition

Vector decomposition involves breaking a vector into components along the coordinate axes. This process is especially helpful in problems where vectors are not aligned with the axes, as it allows one to analyse and calculate the effects along each axis separately. Understanding vector decomposition is crucial when determining the influence of angles on the magnitude and direction of forces in a given coordinate system.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the vector resulting from a cross product. It is particularly useful in determining the direction of the magnetic force on a moving charge. When the velocity is directed using the fingers and the magnetic field is aligned with the palm, the thumb points in the direction of the force for a positive charge; for a negative charge, the force acts in the opposite direction.

Magnetic Force on a Charged Particle

The magnetic force experienced by a charged particle moving in a magnetic field is governed by the Lorentz force law, expressed as F = q(v × B). This force is perpendicular to both the velocity of the particle and the magnetic field. It plays a critical role in the study of electromagnetism and particle motion, as the curvature and trajectory of charged particles in fields are determined by this interaction.

Cross Product

The cross product is an operation on two vectors that yields a third vector perpendicular to the plane containing the original vectors. In the context of magnetism, the magnetic force is calculated as the cross product of the velocity and magnetic field vectors, with the sine of the angle between them determining the magnitude. This mathematical tool is essential for understanding how vector quantities interact in three dimensions.

Please give Ace some feedback