A particle of mass 'm' and charge q is placed at rest in a uniform electric field E and then released. The K.E. attained by the particle after moving a distance y is

 qEy

When a charged particle is placed in a uniform electric field, it experiences a force due to the field.

Let's break this down step by step:

1. Force on the Particle

The force acting on a particle of charge q in an electric field E is given by:

F = qE

This force is responsible for accelerating the particle from rest.

2. Work Done by the Electric Field

Work done on the particle by the electric field when it moves a distance y is:

Work Done (W) = F · y = qE · y

Here, y is the displacement of the particle in the direction of the field. Work done is directly proportional to the distance traveled by the particle and the electric field strength.

3. Relation Between Work Done and Kinetic Energy

According to the Work-Energy Theorem:

Work Done on a particle = Change in its Kinetic Energy

Since the particle starts from rest, its initial kinetic energy is zero. The work done by the electric field is completely converted into the kinetic energy of the particle. Therefore:

Kinetic Energy (K.E.) = W = qE · y

4. Final Expression

The kinetic energy acquired by the particle after moving a distance y in the uniform electric field is:

K.E. = qE · y