The average value of electric energy density in an electromagnetic wave is (`E_(0)` is peak value):

Options

A. `(1)/(2)epsilon_(0)E_(0)^(2)`
B. `(E_(0)^(2))/(2epsilon_(0)`
C. `epsilon_(0)E_(0)^(2)`
D. `(1)/(4)epsilon_(0)E_(0)^(2)`

Explanation

To find the average value of electric energy density in an electromagnetic wave, we can follow these steps:

### Step 1: Understand the formula for electric energy density
The electric energy density (u_E) in an electromagnetic wave is given by the formula:
\[ u_E = \frac{1}{2} \epsilon_0 E^2 \]
where:
- \( \epsilon_0 \) is the permittivity of free space (approximately \( 8.85 \times 10^{-12} \, \text{F/m} \)),
- \( E \) is the electric field strength.

### Step 2: Use the peak value of the electric field
In this case, we are given that \( E_0 \) is the peak value of the electric field. Therefore, we will substitute \( E \) with \( E_0 \) in the formula:
\[ u_E = \frac{1}{2} \epsilon_0 E_0^2 \]

### Step 3: Calculate the average value
The average electric energy density over one complete cycle of the electromagnetic wave can be expressed as:
\[ \langle u_E \rangle = \frac{1}{2} \epsilon_0 E_0^2 \]
This expression represents the average value of the electric energy density in the wave.

### Final Result
Thus, the average value of electric energy density in an electromagnetic wave is:
\[ \langle u_E \rangle = \frac{1}{2} \epsilon_0 E_0^2 \]

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