A charged particle moves under the influence of an electric...

Name: Problem 19, Chapter 27: University Physics with Modern Physics
Uploaded: 2021-05-17T07:24:02-08:00
Duration: 1 min 45 s
Channel: Ajay Singhal
Description: A charged particle moves under the influence of an electric field only. Is it possible for the particle to move with a constant speed? What if the electric field is replaced with a magnetic field?

A charged particle moves under the influence of an electric field only. Is it possible for the particle to move with a constant speed? What if the electric field is replaced with a magnetic field?

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Key Concepts

Work-Energy Principle

The work-energy principle establishes that the work done on an object is equal to its change in kinetic energy. In a situation where a force (like that from an electric field) has a nonzero projection along the velocity of the particle, energy is transferred to or from the particle, resulting in a change in its speed.

Magnetic Field Effects on Charged Particles

A magnetic field exerts a force perpendicular to the velocity of a charged particle (as described by the Lorentz force). Since this force is always orthogonal to the displacement, it does no work on the particle, meaning the kinetic energy and the speed of the particle remain constant, although the direction of the velocity may change, leading to curved trajectories such as circular or helical paths.

Electric Field Effects on Charged Particles

An electric field exerts a force in the direction of the field, which can have a component along the particle’s velocity. This force does work on the particle, changing its kinetic energy and thus its speed. Therefore, under a constant electric field, a charged particle’s speed generally cannot remain constant unless the field or the charge is zero.

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