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) $\frac{2 E^{2} t^{2}}{m q}$ (b) $\frac{E^{2} q^{2} t^{2}}{2 m}$ (c) $\frac{E q^{2} m}{2 t^{2}}$ (d) $\frac{E q m}{2 t}$

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) $\frac{2 E^{2} t^{2}}{m q}$
(b) $\frac{E^{2} q^{2} t^{2}}{2 m}$
(c) $\frac{E q^{2} m}{2 t^{2}}$
(d) $\frac{E q m}{2 t}$

Key Concepts

Electric Field

An electric field is a region of space where a charged particle experiences a force. The magnitude of the force on a charge is determined by the product of the charge and the electric field strength, as described by the equation F = qE. This concept is crucial for understanding how charged particles are accelerated in an electromagnetic environment.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In the context of a charged particle in an electric field, this law is used to relate the force produced by the field to the resulting acceleration of the particle.

Kinematics under Constant Acceleration

When a particle is subject to a constant acceleration, its velocity and displacement over time can be determined using kinematic equations. For a particle starting from rest, the velocity is directly proportional to time (v = at), which is essential for calculating the kinetic energy after a given time period.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. It is defined by the equation KE = 1/2 mv^2, where m is the mass and v is the velocity of the object. In problems involving acceleration (such as in an electric field), substituting the expression for velocity derived from kinematics allows one to find the kinetic energy as a function of time.

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