A particle of mass m and charge q is placed at rest in a uniform electric field E and then released, the kinetic energy attained by the particle after moving a distance y will be

Options

A. `qE y^(2)`
B. `q E y^(2)`
C. `q E y`
D. `q^(2) E y`

Explanation

To find the kinetic energy attained by a particle of mass \( m \) and charge \( q \) after moving a distance \( y \) in a uniform electric field \( E \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Force on the Charged Particle**:
The force \( F \) acting on a charged particle in an electric field is given by:
\[ F = qE \]
where \( q \) is the charge of the particle and \( E \) is the strength of the electric field.

2. **Use Newton's Second Law**:
According to Newton's second law, the acceleration \( a \) of the particle can be expressed as:
\[ a = \frac{F}{m} = \frac{qE}{m} \]

3. **Calculate the Work Done**:
The work done \( W \) on the particle when it moves a distance \( y \) in the direction of the force is:
\[ W = F \cdot y = qE \cdot y \]

4. **Relate Work Done to Kinetic Energy**:
The work-energy principle states that the work done on an object is equal to the change in kinetic energy. Since the particle starts from rest, the initial kinetic energy is zero. Therefore, the kinetic energy \( KE \) attained by the particle after moving a distance \( y \) is:
\[ KE = W = qEy \]

### Final Answer:
Thus, the kinetic energy attained by the particle after moving a distance \( y \) is:
\[ KE = qEy \]