For a plane electromagnetic wave in free space, E(x,t)=E_0 (kx- t)

PHYSICS · Multi-part · CBSE · Physics · Electromagnetic Waves · Electromagnetic Waves

Problem

For a plane electromagnetic wave in free space,

E(x,t)=E_0\cos(kx-\omega t).

Given that the wavelength of the wave is

0.80\,\text{m}

and

E_0=50\,\text{V m}^{-1}

, answer the following: (i) Determine the numerical values of the wave number

k

and angular frequency

\omega

. (ii) Taking

t=2.5\times10^{-9}\,\text{s}

, write the spatial variation of

E

and calculate the positions of the first four nodes (points where

E=0

) measured from

x=0

. Restrict your answer to

x\ge 0

. (iii) Show that the separation between successive nodes obtained in part (ii) equals

\lambda/2