A particle with a charge of 38μC moves with a speed of 77 m / s in the positive x direction. The

step 1 Here we have a particle with a charge of, let's see here, 38 microcologne. It's moving at 77 met

A particle with a charge of 38μC moves with a speed of 77 m...

A particle with a charge of 38$\mu \mathrm{C}$ moves with a speed of 77 $\mathrm{m} / \mathrm{s}$ in the positive $x$ direction. The magnetic field in this region of space has a component of 0.45 $\mathrm{T}$ in the positive $y$ direction, and a component of 0.85 Tin the positive $z$ direction. What are the magnitude and direction of the magnetic force on the particle?

Key Concepts

Lorentz Force Law

The Lorentz force law governs the force experienced by a charged particle moving in electric and magnetic fields. It is encapsulated by the equation F = q(v x B), where q is the particle's charge, v is its velocity, and B is the magnetic field. This concept explains how a magnetic field exerts a force that is perpendicular to both the velocity of the charged particle and the magnetic field itself when there is no electric field present.

Vector Cross Product

The vector cross product is a mathematical operation used to determine a vector that is perpendicular to two given vectors. In the context of the magnetic force on a charged particle, this operation is utilized to compute the force vector by taking the cross product of the velocity and magnetic field vectors. The magnitude of the resulting force is given by the product of the magnitudes of the two vectors and the sine of the angle between them.

Right-Hand Rule

The right-hand rule is a practical tool used to determine the direction of the vector resulting from a cross product. When calculating the magnetic force on a moving charged particle, you point your right-hand fingers in the direction of the velocity vector, curl them toward the magnetic field vector, and your thumb points in the direction of the force experienced by a positive charge.

Magnetic Field Components

Magnetic fields are vector quantities characterized by both magnitude and direction. In problems involving magnetic forces, the magnetic field is often resolved into its components along the coordinate axes. Understanding how to decompose a magnetic field into its individual components is essential for accurately determining the net force acting on a moving charged particle, as the overall force is influenced by each component's contribution.

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