A particle of mass m and charge q is placed at rest in a...

A particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The $\mathrm{KE}$ attained by the particle after moving a distance $y$ is
(a) $q E y^{2}$
(b) $q E^{2} y$
(c) $q E y$
(d) $q^{2} E y$

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Key Concepts

Work-Energy Theorem

The work-energy theorem states that the work done on an object is equal to its change in kinetic energy. For a charged particle moving in a constant electric field, the work done by the electric force (calculated as the force multiplied by the displacement) is converted into the particle's kinetic energy. This is crucial for solving problems that involve energy transfer in electric fields.

Uniform Electric Field

A uniform electric field is one in which the magnitude and direction of the field are constant everywhere. This property simplifies the calculations of forces on charged particles, as the electric force remains constant throughout the particle's motion, leading to straightforward work and energy considerations.

Electric Force

Electric force is the force experienced by a charged particle in an electric field. It is calculated as F = qE, where q is the charge of the particle and E is the electric field strength. This concept explains how charged particles are accelerated and how their motion is influenced by external electric fields.

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