Question

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

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

Answer 1

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

Given: The electric field associated with an electromagnetic wave in vacuum is given by $|\overrightarrow{E}|=40\cos (kz-6\times {10}^{8}t)$

To find: Value of wave vector $k$

Solution:

We know electromagnetic wave eqution is

$|\overrightarrow{E}|=E_0\cos (kz-\omega t)$

And given equation is

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

By comparing these two, we get

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

$E_0=40$

We also know,

Speed of electromagnetic wave is given by:

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

where v is the speed of the light.

Hence,

$k=\frac{\omega }{v}⟹k=\frac{6\times {10}^8}{3\times {10}^8}⟹k=2m^{-1}$

Option $\left(A\right)$ is correct.