Respuesta :
Answer:
magnetic field = - 6.137 × [tex]10^{-7}[/tex] T
Explanation:
given data
radio wave λ = 0.3 m
intensity I = 45 W/m²
time t = 0
time t = 1.5 ns
to find out
What is Bz
solution
we use here equation of intensity of radiation of electric field that is express as
intensity = [tex]\frac{1}{2}c\epsilon_oE_o^2[/tex] .................1
here we know intensity 45 and c is 3 × [tex]10^{8}[/tex] m/s² and ∈o is 8.85 × [tex]10^{-12}[/tex] C²/N.m² and E will be here
E = [tex]\sqrt{\frac{2I}{c\epsilon_o} }[/tex] ...............2
E = [tex]\sqrt{\frac{2*45}{3*10^8 * 8.85*10^{-12}}}[/tex]
E = 184.15
and
E = [tex]c*B_o[/tex] .................3
184.15 = [tex]3.*10^8*B_o[/tex]
[tex]B_o[/tex] = 6.137 × [tex]10^{-7}[/tex] T
and in z axis magnetic field will be here as
B = [tex]B_o* cos(kx - \omega t )[/tex] ..............4
here k = [tex]\frac{2\pi }{\lambda}[/tex]
k = [tex]\frac{2\pi }{0.3}[/tex] = 20.94
and
f = [tex]\frac{c}{\lambda}[/tex]
f = [tex]\frac{3*10^8}{0.3}[/tex] = [tex]10^{9}[/tex]
so here
time t = [tex]\frac{1}{f}[/tex]
t = [tex]\frac{1}{f}[/tex] = [tex]10^{-9}[/tex]
so ω = [tex]\frac{2\pi }{t}[/tex]
ω = [tex]\frac{2\pi }{10^{-9}}[/tex]
ω = 6.28 × [tex]10^{9}[/tex]
so now from equation 4
B = [tex]B_o* cos(kx - \omega t )[/tex]
B = [tex]6.137*10^{-7} *cos(0 - 6.28*10^9*(1.5*10^{-9})[/tex]
B = - 6.137 × [tex]10^{-7}[/tex]
so magnetic field = - 6.137 × [tex]10^{-7}[/tex] T
