Explain why a charged particle moving initially...

Name: Problem 14, Chapter 18: Essential College Physics
Uploaded: 2021-05-30T13:38:24-08:00
Duration: 1 min 45 s
Channel: Ajay Singhal
Description: Explain why a charged particle moving initially perpendicular to a uniform electric field follows a parabolic tra jectory, while a charged particle moving perpendicular to a magnetic field follows a circular tra jectory.

Explain why a charged particle moving initially perpendicular to a uniform electric field follows a parabolic tra jectory, while a charged particle moving perpendicular to a magnetic field follows a circular tra jectory.

Key Concepts

Centripetal Acceleration

Centripetal acceleration is the acceleration required to change the direction of the velocity of an object moving in a circular path. In a magnetic field, because the force is always perpendicular to the velocity of a charged particle, it causes the particle to undergo centripetal acceleration, maintaining circular motion without changing its speed.

Lorentz Force

The Lorentz force law combines the effects of electric and magnetic fields on a charged particle. It shows how the electric force (qE) and the magnetic force (qv × B) influence the particle's motion differently. In an electric field, the force is independent of the velocity, while in a magnetic field the force is always perpendicular to the velocity, leading to distinct trajectories.

Uniform Electric Field

A uniform electric field applies a constant force in a fixed direction, regardless of the particle’s motion. This constant force produces a uniform acceleration in that direction, so when a charged particle starts with a velocity perpendicular to the field, it continues at constant speed in one direction while accelerating in the other, resulting in a parabolic trajectory.

Uniform Magnetic Field

A uniform magnetic field exerts a force on a charged particle that is always perpendicular to its velocity. This perpendicular force does not change the speed of the particle but continuously alters its direction, effectively providing the centripetal force required for circular motion when the initial velocity is perpendicular to the field.

Transcript

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