if `E=E_(0)sin(kz-omegat)` and `B=B_(0)(kz-omegat)` are electric and magnetic field produced by an electromagnetic wave travelling in +z direction in a medium. Then if `eta=(E_(0))/(B_(0))`, then the value of `eta` is `[mu`=permeability of a medium `epsilon=`permittivity of medium]

Options

A. `sqrt(in//H)`
B. `sqrt(mu//en)`
C. `sqrt(mu in)`
D. `(1)/(sqrt(muin))`

Explanation

To find the value of \( \eta = \frac{E_0}{B_0} \) for the given electromagnetic wave equations, we can use the relationship between electric field \( E \), magnetic field \( B \), permeability \( \mu \), and permittivity \( \epsilon \) of the medium.

### Step-by-Step Solution:

1. **Understand the given equations**:
- The electric field is given by \( E = E_0 \sin(kz - \omega t) \).
- The magnetic field is given by \( B = B_0 \sin(kz - \omega t) \).
- Here, \( E_0 \) and \( B_0 \) are the amplitudes of the electric and magnetic fields, respectively.

2. **Use the relationship between electric and magnetic fields**:
- In an electromagnetic wave, the ratio of the electric field to the magnetic field in a medium is given by:
\[ \eta = \frac{E_0}{B_0} \]

3. **Use the energy density concept**:
- The energy density \( u_E \) of the electric field is given by:
\[ u_E = \frac{1}{2} \epsilon E^2 \]
- The energy density \( u_B \) of the magnetic field is given by:
\[ u_B = \frac{1}{2} \frac{B^2}{\mu} \]

4. **Equate the energy densities**:
- For electromagnetic waves, the energy densities of the electric and magnetic fields are equal:
\[ u_E = u_B \]
- Thus, we can write:
\[ \frac{1}{2} \epsilon E_0^2 = \frac{1}{2} \frac{B_0^2}{\mu} \]
- The \( \frac{1}{2} \) cancels out from both sides:
\[ \epsilon E_0^2 = \frac{B_0^2}{\mu} \]

5. **Rearranging the equation**:
- Rearranging gives:
\[ \frac{E_0^2}{B_0^2} = \frac{1}{\mu \epsilon} \]

6. **Taking the square root**:
- Taking the square root of both sides results in:
\[ \frac{E_0}{B_0} = \frac{1}{\sqrt{\mu \epsilon}} \]

7. **Final expression for \( \eta \)**:
- Therefore, we find:
\[ \eta = \frac{E_0}{B_0} = \frac{1}{\sqrt{\mu \epsilon}} \]

### Conclusion:
The value of \( \eta \) is given by:
\[ \eta = \frac{1}{\sqrt{\mu \epsilon}} \]