When :-->
KX + Wt ---> the direction of wave is in negative X direction...
-KX - Wt ---> the direction of wave is in negative X direction...
KX - Wt ---> the direction of wave is in positive X direction...
-KX + Wt ---> the direction of wave is in positive X direction...

So, here both are positive so direction of wave is in negative X direction... that is ( - X)..

$$Hope it's help...$$

Answer:

To determine the direction of propagation of the electromagnetic wave, we need to analyze the given electric field expression:

E = 10cos(10^7 t kx) j^

Here, j^ represents the unit vector along the y-axis.

The wave equation for an electromagnetic wave in free space is given by:

E = E0cos(kx - ωt) j^

Comparing the given expression with the wave equation, we can see that the wave is propagating in the x-direction, which is perpendicular to the y-axis.

Therefore, the correct answer is option b) x.

Explanation:

To understand why the wave is propagating in the x-direction, we need to analyze the wave equation.

The wave equation for an electromagnetic wave is given by:

E = E0cos(kx - ωt) j^

Here,
- E represents the electric field vector
- E0 represents the amplitude of the wave
- k represents the wave number
- x represents the position vector
- ω represents the angular frequency
- t represents time
- j^ represents the unit vector along the y-axis

In the given electric field expression, we have E = 10cos(10^7 t kx) j^.

Comparing this with the wave equation, we can identify the following values:
- E0 = 10
- kx = 10^7 t kx (from the argument of the cosine function)
- ω = 10^7 (angular frequency)

Since the wave equation contains (kx - ωt), and in the given expression we have (10^7 t kx), we can conclude that k = 1 and ω = 10^7.

Now, let's consider the term (kx - ωt):

(kx - ωt) = (1)(x) - (10^7)(t)

From this equation, we can see that the wave is propagating in the x-direction, as the term involving x is positive and the term involving t is negative.

Therefore, the given electromagnetic wave is propagating along the x-direction.