Which one of the following statements concening the energy carried by an electromagnetic wave is true ?

Options

A. The energy is carred only by the electric field .
B. More energy is carried by the electric field than by the magnetic field.
C. The energy is carried equally by the electric and magnetic fields.
D. Moren energy is carried by the magnetic field than by the electric field.

Answer

To determine which statement concerning the energy carried by an electromagnetic wave is true, we need to analyze the relationship between the electric field and the magnetic field in an electromagnetic wave.

### Step-by-Step Solution:

1. **Understanding Electromagnetic Waves**:
- An electromagnetic wave consists of oscillating electric (E) and magnetic (B) fields that are perpendicular to each other and to the direction of wave propagation.

2. **Energy in Electric and Magnetic Fields**:
- The energy density (energy per unit volume) associated with the electric field is given by the formula:
\[ u_E = \frac{1}{2} \epsilon_0 E^2 \]
- The energy density associated with the magnetic field is given by:
\[ u_B = \frac{1}{2} \frac{B^2}{\mu_0} \]

3. **Relationship Between Electric and Magnetic Fields**:
- In an electromagnetic wave, the electric and magnetic fields are related by the equation:
\[ B = \frac{E}{c} \]
- Where \(c\) is the speed of light in a vacuum.

4. **Expressing Magnetic Energy in Terms of Electric Energy**:
- By substituting \(B = \frac{E}{c}\) into the magnetic energy density formula, we get:
\[ u_B = \frac{1}{2} \frac{(E/c)^2}{\mu_0} = \frac{1}{2} \frac{E^2}{\mu_0 c^2} \]
- Since \(c^2 = \frac{1}{\epsilon_0 \mu_0}\), we can rewrite the magnetic energy density as:
\[ u_B = \frac{1}{2} \epsilon_0 E^2 \]

5. **Comparing Energy Densities**:
- From the above expressions, we can see that:
\[ u_E = \frac{1}{2} \epsilon_0 E^2 \quad \text{and} \quad u_B = \frac{1}{2} \epsilon_0 E^2 \]
- This shows that the energy carried by the electric field is equal to the energy carried by the magnetic field.

6. **Conclusion**:
- Since both energy densities are equal, we conclude that the energy is carried equally by the electric and magnetic fields in an electromagnetic wave. Therefore, the correct statement is:
- "The energy is carried equally by the electric and magnetic fields."