Question

The electric field associated with an e.m. wave in vacuum is given by $\overrightarrow{E}=40\cos (kz-6\times {10}^{8}t)\hat{i}$, where $E,z$ and $t$ in $volt/m$, meter and 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 $2m^{-1}$

Given: 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 E, z and t are in volt per meter, meter and second respectively.

To find the value of wave vector k

Solution:

We know electromagnetic wave eqution is

$E=E_0\cos (kz-\omega t)$

And given equation is

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

By comparing these two, we get

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

$E_0=40\hat{i}$

we also know,

Speed of electromagnetic wave, $v=\frac{\omega }{k}$

where v is the speed of the light

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

is the required value