Determine the magnitude and direction of the force on an...

Determine the magnitude and direction of the force on an electron traveling $8.75 \times 10^{5} \mathrm{~m} / \mathrm{s}$ horizontally to the east in a vertically upward magnetic field of strength $0.45 \mathrm{~T}$.

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Key Concepts

Magnetic Lorentz Force

This concept refers to the force experienced by a moving charged particle in a magnetic field, described by the relation F = q(v × B). It involves the charge of the particle, the velocity at which it is moving, and the magnetic field intensity, resulting in a force that is perpendicular to both the velocity and the magnetic field vectors.

Vector Cross Product

The cross product is a mathematical operation applied to two vectors that results in another vector which is perpendicular to the plane containing the original vectors. In the context of the magnetic force, it is used to determine the direction of the force acting on a moving charge relative to the directions of the velocity and the magnetic field.

Right-Hand Rule and the Effect of Charge Sign

The right-hand rule is a mnemonic used to determine the direction of the vector resulting from a cross product. For a positive charge, pointing the fingers along the velocity and curling them toward the magnetic field yields the direction of the force. However, for a negative charge such as an electron, the force is in the opposite direction to that indicated by the rule.

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