Which of the following statement is incorrect about electromagnetic waves?

Options

A. The electric field and magnetic field have equal average values.
B. The electric energy and the magnetic energy have equal average values
C. The electric field and magnetic field both oscillate in same phase
D. The electric field and magnetic field oscillate in opposite phase

Answer

To determine which statement is incorrect about electromagnetic waves, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
The first statement claims that the electric field and the magnetic field have equal average values.

- **Electric Field Average**: The electric field \( E \) of an electromagnetic wave can be represented as:
\[ E = E_0 \sin(kx - \omega t) \]
The average value of \( E \) over one complete cycle is:
\[ \langle E \rangle = 0 \]

- **Magnetic Field Average**: Similarly, the magnetic field \( B \) is given by:
\[ B = B_0 \sin(kx - \omega t) \]
The average value of \( B \) over one complete cycle is:
\[ \langle B \rangle = 0 \]

**Conclusion**: Both average values are equal and are zero. This statement is correct.

### Step 2: Analyze the Second Statement
The second statement states that the electric energy and the magnetic energy have equal average values.

- **Electric Energy Density**: The electric energy density \( u_E \) is given by:
\[ u_E = \frac{1}{2} \epsilon_0 E_0^2 \]

- **Magnetic Energy Density**: The magnetic energy density \( u_B \) is given by:
\[ u_B = \frac{1}{2} \frac{B_0^2}{\mu_0} \]

Using the relationship \( c = \frac{E_0}{B_0} \) and \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \), we can show that:
\[ u_B = \frac{1}{2} \frac{E_0^2}{\mu_0 c^2} = \frac{1}{2} \epsilon_0 E_0^2 \]

**Conclusion**: The average values of electric and magnetic energy densities are equal. This statement is correct.

### Step 3: Analyze the Third Statement
The third statement claims that the electric field and magnetic field both oscillate in the same phase.

From the equations for \( E \) and \( B \):
- Both fields are represented by sinusoidal functions with the same argument \( (kx - \omega t) \).

**Conclusion**: The electric and magnetic fields do oscillate in the same phase. This statement is correct.

### Step 4: Analyze the Fourth Statement
The fourth statement claims that the electric field and magnetic field oscillate in opposite phase.

As established in the previous analysis, both fields oscillate in the same phase, not in opposite phase.

**Conclusion**: This statement is incorrect.

### Final Answer
The incorrect statement about electromagnetic waves is that the electric field and magnetic field oscillate in opposite phase.

---