A charged particle of mass m and charge q is released from...

A charged particle of mass $m$ and charge $q$ is released from rest in an electric field of constant magnitude $E$. The kinetic energy of the particle after time $t$ is (a) $\frac{E^{2} q^{2} t^{2}}{2 m}$ (b) $\frac{2 E^{2} t^{2}}{q m}$ (c) $\frac{\mathrm{Eqm}}{2 t}$ (d) $\frac{E q^{2} m}{2 t^{2}}$

A charged particle of mass $m$ and charge $q$ is released from rest in an electric field of constant magnitude $E$. The kinetic energy of the particle after time $t$ is
(a) $\frac{E^{2} q^{2} t^{2}}{2 m}$
(b) $\frac{2 E^{2} t^{2}}{q m}$
(c) $\frac{\mathrm{Eqm}}{2 t}$
(d) $\frac{E q^{2} m}{2 t^{2}}$

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Key Concepts

Electric Force on a Charged Particle

This concept refers to the force exerted by an electric field on a charged particle, described by Coulomb's Law as F = qE, where q is the charge and E is the magnitude of the electric field. This force dictates the particle’s acceleration in the field.

Newton's Second Law and Acceleration

Newton's second law relates force to acceleration by F = ma. For a charged particle in an electric field, the acceleration is given by a = qE/m, establishing how the mass and charge of the particle affect its motion under a constant field.

Kinematic Equations in Uniform Acceleration

When a particle starts from rest and experiences constant acceleration, its velocity increases linearly with time (v = at). This set of equations allows us to relate displacement, velocity, acceleration, and time for objects moving under constant acceleration.

Kinetic Energy Calculation in Terms of Velocity

The kinetic energy of a moving object is expressed as KE = 1/2 mv^2. By substituting the velocity obtained from the kinematic equations into this formula, one can derive the kinetic energy as a function of time, demonstrating the energy acquired by the particle due to acceleration in the electric field.

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