Question

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.

Answer 1

Here, `lambda=5.0mm=5xx10^-3m,`
`E_0=30Vm^-1`
Angular frequency `omega=2piv=(2pic)/(lambda)`
`=(2xx3.142xx(3xx10^8))/(5xx10^-3)=3.77xx10^11 rad s^-1`
Max. magnitude of magnetic field,
`B_0=(E_0)/c=30/(3xx10^8)=1.0xx10^-7T`
Equation for electric field along y-axis can be
writtens as
`E=E_y=E_0sin omega(t-x//c)`
`=30sin3.77xx10^11(t-x//c)vm^-1`
Equation for magnetic field along z-axis can
be writtens as
`B=B_z=B_0sin omega(t-x//c)`
`=(1.0xx10^-7)sin3.77xx10^11(t-x//C)Tesla`