Question

5) A plane stnusoidal E wve req c4 10o M Ht trave lr through vacum along the 군 direction with max electric field o3.00 mWm directed along the poritive y direction. Find incude al The wavelesgth, Peried, and moximim mag nete fie id valve b) Expressions for electric and magnetic fields as a Mtan。f Units) time, in cludng numerical valves in SI units and n:'t vectors C) The average power per unit area of this wave d) The average energy denr ty of the radhertion (jouler Inm') e) The radiation presture when thir wave refleets perfeetly o1f a surface at nor mal incidence

Answer 1

(a) Frequency = 100 Mhz
wavelength ( $\lambda$ )= C/f = 3*10⁸ /(100*10⁶) = 3 m
Time period = 1/f = 1/(100*10⁶) = 10^-8 s
B_o = E_o/C = 3*10^-3 /(3*10⁸) = 10^-11 T
(b) E = E_o Sin(Kx - wt)
E = 3*10^-3Sin(Kx -wt)
where K = 2Pi/ $\lambda$ = 2.094
w = 2Pif = 2Pi*10⁸ = 6.283*10⁸
E = 3*10^-3Sin(2.094x - 6.283*10⁸ t)
Similarly
B = B_oSin(Kx - wt)
B = 10^-11Sin(2.094x - 6.283*10⁸ t)
(c) Power per unit area is Intensity
I = EB/ $\mu _{o}$
I = 3*10^-3*10^-11 / (4Pi*10^-7) = 2.387*10^-8 W/m²
(d) Energy density = I/C = 2.387*10^-8 /(3*10⁸) = 7.957*10^-17 J/m³
(e) Radiation pressure is also defined by = intensity /C = 7.957*10^-17 N/m²