During the propagation of electromagnetic waves in a medium :

Options

A. Both electric and magnetic energy densitites are zero
B. Electric energy density is half of the magnetic energy density .
C. Electric energy density is half of the magnetic energy density .
D. Electric energy density is equal to the magnetic energy density

Answer

To solve the question regarding the relationship between the electric and magnetic energy densities during the propagation of electromagnetic waves in a medium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Energy Densities**:
- The electric energy density (u_E) in a medium is given by the formula:
\[ u_E = \frac{1}{2} \epsilon_0 E^2 \]
- The magnetic energy density (u_B) is given by:
\[ u_B = \frac{1}{2} \frac{B^2}{\mu_0} \]

2. **Relation between Electric and Magnetic Fields**:
- In electromagnetic waves, the electric field (E) and magnetic field (B) are related by:
\[ B = \frac{E}{c} \]
- Here, \( c \) is the speed of light in the medium, which can also be expressed as:
\[ c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \]

3. **Substituting B in the Magnetic Energy Density**:
- Substitute \( B \) in the magnetic energy density formula:
\[ u_B = \frac{1}{2} \frac{\left(\frac{E}{c}\right)^2}{\mu_0} \]
- This simplifies to:
\[ u_B = \frac{1}{2} \frac{E^2}{c^2 \mu_0} \]

4. **Using the Relation between c, ε₀, and μ₀**:
- Since \( c^2 = \frac{1}{\epsilon_0 \mu_0} \), we can replace \( \mu_0 \) in the equation:
\[ u_B = \frac{1}{2} \frac{E^2}{\frac{1}{\epsilon_0}} = \frac{1}{2} \epsilon_0 E^2 \]

5. **Comparing Electric and Magnetic Energy Densities**:
- Now we have:
\[ u_E = \frac{1}{2} \epsilon_0 E^2 \]
\[ u_B = \frac{1}{2} \epsilon_0 E^2 \]
- Therefore, we conclude that:
\[ u_E = u_B \]

6. **Final Conclusion**:
- The electric energy density is equal to the magnetic energy density in an electromagnetic wave propagating through a medium.

### Answer:
The correct option is that the electric energy density is equal to the magnetic energy density.