A plane electromagnetic wave propagating in the x-direction has a wavelength of 5.0 mm. The electric field is in the y-direction and its maximum magnitude is `30V (m^-1)`. Write suitable equations for the electric and magnetic fields as a function of x and t.

Explanation

Given, `lambda=5mm=5xx10^-3m`
` k=(2pi)/lambda =(2pi)/(5xx10^-3)m^-1`
` = 1257m^-1`
From the equation,
`c = omega/k`
`omega = c k= (3xx10^8)(1257)`
`3.77xx10^11 rad//s`
`E_0=30 V//m`
`c = E_0/B_0`
`B_0=E_0/c = 30/3xx10^8`
`10^-7 T`
Now,
`E_y=E_0 sin (omegat-kx)`
`(30 V// m) sin [3.77xx10^11 s^-1)t-(1257m^-1)x]`
and ` B_z=(10^-7 T) sin [3.77xx10^11 8^-1)t-(1257,^-1)x]`.