Show that the average energy density of the electric field `vecE` equals the average energy density of the magnetic field `vecB`, in electromagnetic waves.

Explanation

To show that the average energy density of the electric field \( \vec{E} \) equals the average energy density of the magnetic field \( \vec{B} \) in electromagnetic waves, we can follow these steps:

### Step 1: Define the average energy density of the electric field
The average energy density \( U_E \) of the electric field is given by the formula:
\[ U_E = \frac{1}{2} \epsilon_0 E_{\text{rms}}^2 \]
where \( \epsilon_0 \) is the permittivity of free space and \( E_{\text{rms}} \) is the root mean square value of the electric field.
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