Answer to Question #105179 in Electricity and Magnetism for jeevan Jyoti behera

Question

Is it true? The electric field associated with a plane electromagnetic wave is given by E=50 cos(wt-10πx)z bar V/m.its wavelength is 0.5m

Answer 1

A plane electromagnetic wave with the direction of wave propagation along $x$ axis is described by the following equation

(1) $\vec E(t,x)=\hat z E_acos(wt-kx)$, where $k=\frac{2\pi}{\lambda}$ is a component of wave vector in $x$ direction. In our case $k=10\pi$, thus $\frac{2\pi}{\lambda}=10\pi$ and $\lambda=\frac{1}{5}=0.2 m$.

Answer: The task statement is false. It is true $\lambda=0.2m$ .