A charge q is placed in an uniform electric field E. If it is released, then the K.E of the charge after travelling distance y will be :

Options

A. qEy
B. 2qEy
C. `(qEy)/2`
D. `sqrt(qEy)`

Explanation

To find the kinetic energy of a charge \( q \) after it has traveled a distance \( y \) in a uniform electric field \( E \), we can use the work-energy theorem. Here are the steps to derive the solution:

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- The charge \( q \) is initially at rest in the electric field. Therefore, the initial kinetic energy \( KE_1 = 0 \).

2. **Apply the Work-Energy Theorem**:
- The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy:
\[ W = \Delta KE = KE_2 - KE_1 \]
- Since \( KE_1 = 0 \), we can simplify this to:
\[ W = KE_2 \]

3. **Calculate the Work Done**:
- The work done \( W \) by the electric field on the charge as it moves through a distance \( y \) can be calculated using the formula:
\[ W = F \cdot d \]
- Here, \( F \) is the electric force acting on the charge, which can be expressed as:
\[ F = qE \]
- Therefore, the work done can be rewritten as:
\[ W = qE \cdot y \]

4. **Relate Work Done to Kinetic Energy**:
- From the work-energy theorem, we have:
\[ KE_2 = W = qE \cdot y \]

5. **Final Expression for Kinetic Energy**:
- Thus, the kinetic energy of the charge after traveling a distance \( y \) in the electric field \( E \) is:
\[ KE = qEy \]

### Final Answer:
The kinetic energy of the charge after traveling a distance \( y \) is given by:
\[ KE = qEy \]