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)`

Answer

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

### Step 1: Understand the concept of electrostatic energy density
Electrostatic energy density (u) is defined as the energy stored per unit volume in an electric field.

### Step 2: Recall the formula for electrostatic energy density
The formula for electrostatic energy density is given by:
\[ u = \frac{1}{2} \epsilon_0 E^2 \]
where:
- \( u \) is the energy density,
- \( \epsilon_0 \) is the permittivity of free space (a constant),
- \( E \) is the electric field intensity.

### Step 3: Analyze the formula
From the formula \( u = \frac{1}{2} \epsilon_0 E^2 \), we can see that the energy density \( u \) is directly proportional to the square of the electric field intensity \( E \).

### Step 4: Determine the proportionality
Since \( \epsilon_0 \) is a constant, we can conclude that:
\[ u \propto E^2 \]

### Conclusion
Thus, the electrostatic energy density is proportional to the square of the electric field intensity. Therefore, the correct answer is:
\[ \text{Electrostatic energy density is proportional to } E^2. \]