The magnetic field of Earth at a certain location is...

The magnetic field of Earth at a certain location is directed vertically downward and has a magnitude of $50.0 \mu \mathrm{T}$. A proton is moving horizontally toward the west in this field with a speed of $6.20 \times 10^{6} \mathrm{~m} / \mathrm{s}$. What are the direction and magnitude of the magnetic force the field exerts on the proton?

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Key Concepts

Magnetic Field

A magnetic field is a vector field that exerts a force on moving electric charges as well as on magnetic dipoles. It is characterized by both a magnitude and a direction, and it plays a central role in phenomena such as electromagnetism and magnetic forces.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field. It is given by the equation F = q(V × B), where q is the charge, V is the velocity vector of the particle, and B is the magnetic field vector. This force is always perpendicular to both the velocity of the particle and the magnetic field.

Cross Product

The cross product is a mathematical operation on two vectors that results in a new vector perpendicular to the plane containing the original vectors. Its magnitude is given by the product of the magnitudes of the original vectors and the sine of the angle between them, which is crucial for determining the magnitude of the magnetic force on a charged particle.

Right-Hand Rule

The right-hand rule is a technique used to determine the direction of the vector resulting from a cross product. For a positively charged particle, if you point your fingers in the direction of the velocity vector and curl them toward the magnetic field vector, your thumb points in the direction of the magnetic force acting on the particle.

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