Question

The electric field associated with an electromagnetic wave in vacuum is given by, $\overrightarrow{E}=40\cos (kz-6\times {10}^{8}t)\hat{i}$, where all quantities are in SI units. The value of $k$ is -

• A. $2{\text{m}}^{-1}$
• B. $3{\text{m}}^{-1}$
• C. $4{\text{m}}^{-1}$
• D. $5{\text{m}}^{-1}$

Answer 1

The correct option is A $2{\text{m}}^{-1}$

Given:

$\overrightarrow{E}=40\cos (kz-6\times {10}^{8}t)\hat{i}$

On comparing this equation with, $\overrightarrow{E}=E_0\cos (kz-\omega t)\hat{i}$, we get,

$\omega =6\times {10}^8\text{rad/s}$

Now, we know that, speed of electromagnetic wave,

$c=\frac{\omega }{k}$

$\Rightarrow k=\frac{\omega }{c}=\frac{6\times {10}^8}{3\times {10}^8}=2{\text{m}}^{-1}$

Hence, option $\left(A\right)$ is the correct answer.