Question

The electric field associated with an e.m wave in vacuum is given by $\overrightarrow{E}=\hat{i}40\cos (kz-6\times {10}^{8}t)$,
where E,z and t are in volt/m,meter ans seconds respectively.The value of wave vector k is:

• A. $6m^{-1}$
• B. $3m^{-1}$
• C. $2m^{-1}$
• D. $0.5m^{-1}$

Answer 1

The correct option is C $2m^{-1}$

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

A general form of electric vector is:

$\overrightarrow{E}={\overrightarrow{E}}_0\cos (\hat{k}.\hat{r}-\omega t)$

comparing this equation with above equation

$\omega =6\times {10}^8$

Here a $\omega$ is frequency , $\left|\overrightarrow{E_0}\right|$ is electric field amplitude and $\overrightarrow{k}$ is the wave vector.Also for electromagnetic waves:

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