Show that the avearge 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: Write the formula for average energy density of the electric field
The average energy density \(u_E\) of the electric field in an electromagnetic wave is given by the formula:
\[ u_E = \frac{1}{2} \epsilon_0 E_0^2 \]
where \(E_0\) is the maximum (peak) value of the electric field, and \(\epsilon_0\) is the permittivity of free space.
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