Understanding Lorentz's Law for Magnetic Force

The question asks to identify the specific law that describes the force (denoted as $\vec{F}$) acting on a charged particle with charge q, as it moves with a certain velocity ($\vec{v}$) through a magnetic field (denoted as $\vec{B}$).

Exploring the Relevant Physics Laws

Let's examine the provided options to determine which law accurately represents this interaction:

• Faraday's Law: This law explains how a changing magnetic field induces an electromotive force (EMF), which in turn can create an electric field. It's fundamental to understanding electromagnetic induction but doesn't directly describe the force on a single moving charged particle in a given magnetic field.
• Biot-Savart Law: This law is used to calculate the magnetic field ($\vec{B}$) generated by a steady electric current or a moving charge. It helps determine the magnetic field itself, not the force experienced by a particle within that field.
• Coulomb's Law: This law governs the electrostatic force between two stationary electric charges. It deals with forces due to electric fields, not magnetic fields acting on moving charges.
• Lorentz's Law: This is the correct law. Lorentz's law describes the total force experienced by a charged particle due to both electric and magnetic fields.

Lorentz's Law Explained

Lorentz's law combines the effects of electric and magnetic fields on a charged particle. The complete formula for the Lorentz force is:

Where:

• $\vec{F}$ is the total force experienced by the particle.
• $q$ is the charge of the particle.
• $\vec{E}$ is the electric field at the particle's location.
• $\vec{v}$ is the velocity of the particle.
• $\vec{B}$ is the magnetic field at the particle's location.
• $\vec{v} \times \vec{B}$ represents the cross product of the velocity and magnetic field vectors.

In the specific context of the question, which focuses on the force experienced while moving through a magnetic field $\vec{B}$ with velocity $\vec{v}$, we are interested in the magnetic force component of the Lorentz law. If we assume there is no electric field ($\vec{E} = 0$), the equation simplifies to the magnetic force:

This formula precisely describes the force ($\vec{F}$) on a charged particle ($q$) moving with velocity ($\vec{v}$) in a magnetic field ($\vec{B}$). Therefore, Lorentz's law is the law that fits the description.