In the following question a statement of assertion (A) is followed by a statement of reason (R )
A: If E be electric field at a point , in free space then energy density at that point will be `(1)/(2) epsilon_(0)E^(2)` .
R , electrostatic field is a conservative field .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1).
B. If both Assertion & Reason are true but the reason is not correct explanation of the assertion then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements , then mark (4).

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided in the problem.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that if \( E \) is the electric field at a point in free space, then the energy density at that point is given by the formula:
\[ u = \frac{1}{2} \epsilon_0 E^2 \]
- Here, \( \epsilon_0 \) is the permittivity of free space.

2. **Deriving the Energy Density**:
- The energy density \( u \) is defined as the energy stored per unit volume in an electric field.
- For a capacitor, the energy \( U \) stored can be expressed as:
\[ U = \frac{1}{2} C V^2 \]
- The capacitance \( C \) can be expressed in terms of the permittivity of free space \( \epsilon_0 \):
\[ C = \frac{\epsilon_0 A}{d} \]
- Here, \( A \) is the area of the plates and \( d \) is the separation between them.

3. **Relating Voltage and Electric Field**:
- The voltage \( V \) across the capacitor can be related to the electric field \( E \) as:
\[ V = E \cdot d \]
- Substituting this into the energy formula gives:
\[ U = \frac{1}{2} \left( \frac{\epsilon_0 A}{d} \right) (E \cdot d)^2 = \frac{1}{2} \epsilon_0 A \frac{E^2 d^2}{d^2} = \frac{1}{2} \epsilon_0 A E^2 \]

4. **Calculating Energy Density**:
- The volume \( V \) of the capacitor is given by \( A \cdot d \).
- Therefore, the energy density \( u \) can be calculated as:
\[ u = \frac{U}{\text{Volume}} = \frac{\frac{1}{2} \epsilon_0 A E^2}{A \cdot d} = \frac{1}{2} \epsilon_0 E^2 \]
- This confirms that the assertion \( A \) is correct.

5. **Understanding the Reason (R)**:
- The reason states that the electrostatic field is a conservative field.
- A conservative field implies that the work done in moving a charge between two points is independent of the path taken. This is true for electrostatic fields.

6. **Evaluating the Relationship**:
- While both the assertion and reason are true, the reason does not directly explain the assertion. The assertion is about the energy density formula, while the reason is about the nature of the electrostatic field.

### Conclusion:
- The assertion is correct, and the reason is also correct, but the reason does not explain the assertion. Therefore, the correct option is that both statements are true, but the reason is not the correct explanation for the assertion.