Question

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

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

Answer 1

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

Comparing the given equation with
$E=E_0\cos (kz—\omega t)$
we get, $\omega =6\times {10}^8{s}^{-1}$
Wave vector
$k=\frac{\omega }{c}=\frac{6\times {10}^8{s}^{-1}}{3\times {10}^{8}m{s}^{-1}}=2m^{-1}$