One component of a magnetic field has a magnitude of 0.048 T and points along the +x axis, while

step 1 problem we have given one component of magnetic field is 0 .04a Tesla and the direction is along

One component of a magnetic field has a magnitude of 0.048 T...

One component of a magnetic field has a magnitude of $0.048 \mathrm{T}$ and points along the $+x$ axis, while the other component has a magnitude of $0.065 \mathrm{T}$ and points along the $-y$ axis. A particle carrying a charge of $+2.0 \times 10^{-5} \mathrm{C}$ is moving along the $+z$ axis at a speed of $4.2 \times \mathrm{x}$ $10^{3} \mathrm{m} / \mathrm{s}$ (a) Find the magnitude of the net magnetic force that acts on the particle. (b) Determine the angle that the net force makes with respect to the $+x$ axis.

One component of a magnetic field has a magnitude of $0.048 \mathrm{T}$ and points along the $+x$ axis, while the other component has a magnitude of $0.065 \mathrm{T}$ and points along the $-y$ axis. A particle carrying a charge of $+2.0 \times 10^{-5} \mathrm{C}$ is moving along the $+z$ axis at a speed of $4.2 \times \mathrm{x}$ $10^{3} \mathrm{m} / \mathrm{s}$ (a) Find the magnitude of the net magnetic force that acts on the particle.
(b) Determine the angle that the net force makes with respect to the $+x$ axis.

Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in an electromagnetic field. In the magnetic case, it is given by the equation F = q(v × B), where q is the charge, v is the velocity vector, and B is the magnetic field vector. This concept is fundamental in understanding how magnetic fields interact with moving charges and how the direction and magnitude of the force are determined by the cross product of the velocity and magnetic field vectors.

Vector Cross Product

The vector cross product is a mathematical operation that returns a vector perpendicular to the plane defined by the two input vectors. In the context of magnetic forces, the cross product v × B determines not only the magnitude of the magnetic force but also its direction, which follows the right-hand rule. This operation is essential in analyzing how different vector components contribute to the net force on a charged particle in a magnetic field.

Magnetic Field Components

Magnetic fields in many physical problems are often expressed as the sum of multiple components in different directions. Each component contributes to the overall magnetic force when interacting with a moving charged particle. Understanding how to combine these components using vector addition is critical for accurately determining the net magnetic field that influences the particle.

Vector Magnitude and Angle Calculation

Calculating the magnitude and direction (angle) of a resultant vector involves breaking it into its components and using trigonometric relationships. In scenarios where a force or field is composed of orthogonal components, the Pythagorean theorem is used to determine the magnitude, and inverse trigonometric functions are employed to find the angle it makes with a given axis. These techniques are widely applicable in physics to analyze the behavior of vectors in two or three dimensions.

Transcript

Please give Ace some feedback