If `E` is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

Options

A. `E`
B. `E^(2)`
C. `1//E^(2)`
D. `E^(3)`

Explanation

To solve the question regarding the relationship between electric field intensity \( E \) and electrostatic energy density, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Field Intensity**:
- The electric field intensity \( E \) is a measure of the force experienced by a unit positive charge placed in the field. It is a vector quantity.

2. **Defining Electrostatic Energy Density**:
- Electrostatic energy density is defined as the energy stored per unit volume in an electric field. It is denoted as \( \frac{dU}{dV} \), where \( U \) is the potential energy and \( V \) is the volume.

3. **Formula for Electrostatic Energy Density**:
- The formula for electrostatic energy density in an electric field is given by:
\[ \text{Energy Density} = \frac{1}{2} \epsilon_0 E^2 \]
- Here, \( \epsilon_0 \) is the permittivity of free space, and \( E \) is the electric field intensity.

4. **Identifying Proportionality**:
- From the formula \( \frac{1}{2} \epsilon_0 E^2 \), we can see that the energy density is proportional to the square of the electric field intensity \( E \).
- This means:
\[ \text{Energy Density} \propto E^2 \]

5. **Conclusion**:
- Therefore, the electrostatic energy density is proportional to \( E^2 \).

### Final Answer:
The electrostatic energy density is proportional to \( E^2 \).

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