Which of the following have zero average value in a plane electromagnetic wave?

Options

A. electric field
B. magnetic field
C. electric energy
D. magnetic energy.

Answer

To solve the question of which quantities have a zero average value in a plane electromagnetic wave, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Plane Electromagnetic Waves**:
- A plane electromagnetic wave consists of oscillating electric and magnetic fields that propagate through space. The electric field (E) and magnetic field (B) oscillate sinusoidally.

2. **Mathematical Representation**:
- For a plane wave propagating in the z-direction, the electric field can be expressed as:
\[ E(z, t) = E_0 \sin(kz - \omega t) \]
- Similarly, the magnetic field can be represented as:
\[ B(z, t) = B_0 \sin(kz - \omega t) \]

3. **Calculating Average Values**:
- The average value of a sinusoidal function over a complete cycle is zero. This is because the positive and negative halves of the sine wave cancel each other out.
- Therefore, the average value of the electric field \( \langle E \rangle \) and the average value of the magnetic field \( \langle B \rangle \) are both zero:
\[ \langle E \rangle = 0 \quad \text{and} \quad \langle B \rangle = 0 \]

4. **Considering Electric and Magnetic Energy**:
- The electric energy density \( u_E \) and magnetic energy density \( u_B \) in an electromagnetic wave are given by:
\[ u_E = \frac{1}{2} \epsilon_0 E^2 \quad \text{and} \quad u_B = \frac{1}{2} \frac{B^2}{\mu_0} \]
- Since \( E \) and \( B \) oscillate, their squares \( E^2 \) and \( B^2 \) will also oscillate, but they will not average to zero over a complete cycle. Instead, they will have a positive average value.

5. **Conclusion**:
- The quantities that have a zero average value in a plane electromagnetic wave are the electric field and the magnetic field. Therefore, the correct options are:
- Electric Field (Option 1)
- Magnetic Field (Option 2)

### Final Answer:
The quantities that have zero average value in a plane electromagnetic wave are:
- Electric Field (Option 1)
- Magnetic Field (Option 2)