In a plane electromagnetic wave which of the following have zero average value ?

Options

A. Magnetic field
B. Magnetic energy
C. Electric field
D. Electric energy

Answer

To determine which quantities have a zero average value in a plane electromagnetic wave, we will analyze the electric field (E) and the magnetic field (B) of the wave.

### Step-by-Step Solution:

1. **Understanding the Electric Field**:
- The electric field of a plane electromagnetic wave can be expressed as:
\[ E = E_0 \sin(kx - \omega t) \]
- Here, \(E_0\) is the amplitude of the electric field, \(k\) is the wave number, \(x\) is the position, \(\omega\) is the angular frequency, and \(t\) is time.

2. **Calculating the Average Value of the Electric Field**:
- The average value of a sinusoidal function over one complete cycle is given by:
\[ \text{Average}(E) = \frac{1}{T} \int_0^T E \, dt \]
- For the sine function, the average value over one complete cycle (period \(T\)) is zero because the positive and negative halves cancel each other out:
\[ \text{Average}(E) = 0 \]

3. **Understanding the Magnetic Field**:
- The magnetic field of a plane electromagnetic wave can be expressed similarly:
\[ B = B_0 \sin(kx - \omega t) \]
- Here, \(B_0\) is the amplitude of the magnetic field.

4. **Calculating the Average Value of the Magnetic Field**:
- Using the same reasoning as for the electric field, the average value of the magnetic field over one complete cycle is also zero:
\[ \text{Average}(B) = 0 \]

5. **Conclusion**:
- Both the electric field \(E\) and the magnetic field \(B\) have zero average values in a plane electromagnetic wave.

### Final Answer:
In a plane electromagnetic wave, both the electric field and the magnetic field have zero average values.