A uniform magnetic field points north; its magnitude is 1.5 T . A proton with kinetic energy 8.0

step 1 In this problem a uniform magnetic field points north and its magnitude is 1 .5 tesla and a prot

A uniform magnetic field points north; its magnitude is 1.5...

A uniform magnetic field points north; its magnitude is $1.5 \mathrm{T} .$ A proton with kinetic energy $8.0 \times 10^{-13} \mathrm{J}$ is moving vertically downward in this field. What is the magnetic force acting on it?

Key Concepts

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in a magnetic field and is given by the equation F = q(v × B). This concept is fundamental in electromagnetism as it relates the charge, its velocity, and the external magnetic field through the cross product, meaning the force acts perpendicular to both the velocity and the magnetic field vectors.

Uniform Magnetic Field

A uniform magnetic field is one in which both the magnitude and direction of the magnetic field remain constant throughout the space in consideration. This constant characteristic simplifies calculations of magnetic forces on moving charges because the field does not change with position.

Conversion of Kinetic Energy to Velocity

The relationship between kinetic energy and the speed of a particle is given by the equation KE = 0.5mv². This conversion is crucial in problems involving forces on moving charges, where knowing the speed is required to compute the magnitude of the force acting on the charged particle.

Cross Product in Vector Calculations

The cross product is a mathematical operation used in vector calculations to determine a vector that is perpendicular to two given vectors. In the context of magnetic forces, it ensures that the magnetic force is always oriented perpendicular to both the velocity of the charge and the magnetic field.

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