The magnitude of electric intensity at a distance `x` from a charge `q` is `E`.An identical charge is placed at a distance `2x` from it Then the magnitude of the force it experience is ..

Options

A. qE
B. 2qE
C. `(qE)/(2)`
D. `(qE)/(4)`

Explanation

To solve the problem step by step, we will follow the concepts of electric field intensity and the force experienced by a charge in an electric field.

### Step 1: Understand Electric Field Intensity
The electric field intensity \( E \) at a distance \( x \) from a point charge \( q \) is given by the formula:
\[ E = \frac{kq}{x^2} \]
where \( k \) is Coulomb's constant.

### Step 2: Given Information
We know that at a distance \( x \) from charge \( q \), the electric field intensity is \( E \). Therefore, we can write:
\[ E = \frac{kq}{x^2} \]

### Step 3: Identify the New Charge Position
An identical charge \( q \) is placed at a distance \( 2x \) from the original charge \( q \). We need to find the electric field intensity at this new position.

### Step 4: Calculate Electric Field Intensity at Distance \( 2x \)
Using the formula for electric field intensity, we can calculate the electric field intensity \( E' \) at a distance \( 2x \):
\[ E' = \frac{kq}{(2x)^2} = \frac{kq}{4x^2} \]

### Step 5: Relate \( E' \) to \( E \)
Since we know that \( E = \frac{kq}{x^2} \), we can express \( E' \) in terms of \( E \):
\[ E' = \frac{1}{4} \cdot \frac{kq}{x^2} = \frac{E}{4} \]

### Step 6: Calculate the Force Experienced by the Charge
The force \( F \) experienced by a charge \( q \) in an electric field \( E' \) is given by:
\[ F = qE' \]
Substituting \( E' \) into the formula:
\[ F = q \cdot \frac{E}{4} = \frac{qE}{4} \]

### Conclusion
Thus, the magnitude of the force experienced by the charge placed at a distance \( 2x \) from the original charge is:
\[ F = \frac{qE}{4} \]