The electric field associated with an electromagnetic wave in vacuum is given by `vecE=40cos(kz-6xx10^(8)t)hati,`
where E, z and t are in volt per meter, meter and second respectively. The value of wave vector k is

Options

A. `2 m^(-1)`
B. `0.5 m^(-1)`
C. `6 m^(-1)`
D. `3 m^(-1)`

Explanation

To find the value of the wave vector \( k \) from the given electric field expression \( \vec{E} = 40 \cos(kz - 6 \times 10^8 t) \hat{i} \), we can follow these steps:

### Step 1: Identify the angular frequency \( \omega \)
From the expression \( \vec{E} = 40 \cos(kz - 6 \times 10^8 t) \hat{i} \), we can see that the term associated with time \( t \) is \( -6 \times 10^8 t \). This term represents the angular frequency \( \omega \).

\[ \omega = 6 \times 10^8 \, \text{rad/s} \]

### Step 2: Use the relationship between wave speed, angular frequency, and wave vector
The relationship between wave speed \( v \), angular frequency \( \omega \), and wave vector \( k \) is given by:

\[ v = \frac{\omega}{k} \]

### Step 3: Substitute the speed of light for \( v \)
In a vacuum, the speed of electromagnetic waves is equal to the speed of light \( c \), which is approximately:

\[ c = 3 \times 10^8 \, \text{m/s} \]

### Step 4: Rearrange the equation to solve for \( k \)
We can rearrange the equation to solve for \( k \):

\[ k = \frac{\omega}{v} \]

Substituting the values we have:

\[ k = \frac{6 \times 10^8}{3 \times 10^8} \]

### Step 5: Calculate \( k \)
Now, perform the calculation:

\[ k = 2 \, \text{m}^{-1} \]

### Final Answer
Thus, the value of the wave vector \( k \) is:

\[ \boxed{2 \, \text{m}^{-1}} \]

---