The electric field part of an electromagnetic wave in a medium is represented by
`E_(x)=0,`
`E_(y)=2.5(N)/(C) cos[(2pixx10^(6)(rad)/(m))t-(pixx10^(-2)(rad)/(s))x]`
`E_(z)=0`.
The wave is

Options

A. moving along y-direction with frequency `2pixx10^(6)Hz` and wavelength `200m`.
B. moving along x-direction with frequency `10^(6)Hz` and wavelength `100m`
C. moving along x-direction with frequency `10^(6)Hz` and wavelength `100m`
D. moving along x-direction with frequency `10^(6)Hz` and wavelength `200m`

Explanation

To solve the problem, we need to analyze the given electric field expression of the electromagnetic wave and extract information about its direction of propagation, frequency, and wavelength.

### Step-by-Step Solution:

1. **Identify the Electric Field Components:**
The electric field components are given as:
\[ E_x = 0, \quad E_y = 2.5 \, \text{N/C} \cos\left[(2\pi \times 10^6 \, \text{rad/m}) t - (\pi \times 10^{-2} \, \text{rad/s}) x\right], \quad E_z = 0 \]
This indicates that the electric field is oriented along the y-axis.

2. **Compare with the General Wave Equation:**
The general form of the electric field of a wave is:
\[ E = E_0 \cos(\omega t - kx) \]
Here, we can identify:
- \( E_0 = 2.5 \, \text{N/C} \)
- \( \omega = 2\pi \times 10^6 \, \text{rad/s} \)
- \( k = \pi \times 10^{-2} \, \text{rad/m} \)

3. **Determine the Direction of Propagation:**
The wave is propagating in the direction of the wave vector \( k \). Since \( kx \) is subtracted in the wave equation, the wave is moving in the positive x-direction.

4. **Calculate the Frequency:**
The frequency \( f \) can be calculated using the relation:
\[ f = \frac{\omega}{2\pi} \]
Substituting the value of \( \omega \):
\[ f = \frac{2\pi \times 10^6}{2\pi} = 10^6 \, \text{Hz} \]

5. **Calculate the Wavelength:**
The wavelength \( \lambda \) can be calculated using the relation:
\[ k = \frac{2\pi}{\lambda} \]
Rearranging gives:
\[ \lambda = \frac{2\pi}{k} \]
Substituting the value of \( k \):
\[ \lambda = \frac{2\pi}{\pi \times 10^{-2}} = 200 \, \text{m} \]

6. **Summarize the Results:**
- The wave is propagating in the positive x-direction.
- The frequency of the wave is \( 10^6 \, \text{Hz} \).
- The wavelength of the wave is \( 200 \, \text{m} \).

### Final Answer:
The wave is propagating in the positive x-direction with a frequency of \( 10^6 \, \text{Hz} \) and a wavelength of \( 200 \, \text{m} \).