Question

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

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

Answer 1

Answer: (A)

$2\, m^{-1}$

Answer 2

Equation of Electromagnetic wave is $E = E _{0} \cos ( kz -\omega t )$ and speed of EM wave $V =\frac{\omega}{ k }$ By comparing $k =\omega / v =\frac{6 \times 10^{8}}{3 \times 10^{8}}=2 m ^{-1}$ is the wave vector.