Electric field of an electromagnetic wave travelling in vacuum is given by
` E = 20 sin ( kx - 6 xx 10^(8 ) t)`
what should the value of k in SI units ?

Explanation

To find the value of \( k \) in SI units for the given electric field of an electromagnetic wave, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given electric field equation**:
The electric field of the electromagnetic wave is given by:
\[ E = 20 \sin(kx - 6 \times 10^8 t) \]

2. **Compare with the standard form**:
The standard form of the electric field for an electromagnetic wave is:
\[ E = E_0 \sin(kx - \omega t) \]
From this, we can identify:
- \( \omega = 6 \times 10^8 \) rad/s
- \( k \) is what we need to find.

3. **Relate angular frequency to frequency**:
The angular frequency \( \omega \) is related to the frequency \( \nu \) by the formula:
\[ \omega = 2\pi\nu \]
Therefore, we can find \( \nu \):
\[ \nu = \frac{\omega}{2\pi} = \frac{6 \times 10^8}{2\pi} \]

4. **Use the speed of light**:
The speed of light \( c \) in a vacuum is given by:
\[ c = \nu \lambda \]
where \( \lambda \) is the wavelength. We can express \( \nu \) in terms of \( c \) and \( \lambda \):
\[ \nu = \frac{c}{\lambda} \]

5. **Combine the equations**:
From the previous steps, we can substitute \( \nu \) into the equation for \( k \):
\[ k = \frac{2\pi\nu}{c} \]
Substituting \( \nu = \frac{6 \times 10^8}{2\pi} \):
\[ k = \frac{2\pi \left(\frac{6 \times 10^8}{2\pi}\right)}{c} \]

6. **Substituting the value of \( c \)**:
The speed of light \( c \) is approximately \( 3 \times 10^8 \) m/s. Therefore:
\[ k = \frac{6 \times 10^8}{3 \times 10^8} \]

7. **Calculate \( k \)**:
\[ k = 2 \text{ m}^{-1} \]

### Final Answer:
The value of \( k \) in SI units is:
\[ k = 2 \text{ m}^{-1} \]