Respuesta :
Answer:
power = 600000 W
intensity = 6666666.66 W/m²
Em = 70880.18 N/m
F = 2 × [tex]10^{-3}[/tex] N
Explanation:
given data
frequency f = 2400 MHz
height oven cavity h = 25 cm = 0.25 m
base area measures A = 30 cm by 30 cm
total microwave energy content of cavity E = 0.50 mJ = 0.50 × [tex]10^{-3}[/tex]
solution
first, we get here total time taken from top to bottom that is express as
Δt = [tex]\frac{h}{c}[/tex] ...............1
Δt = [tex]\frac{0.25}{3\times 10^8}[/tex]
Δt = 8.33 × [tex]10^{-10}[/tex] s
and
power output will be
power = [tex]\frac{E}{\Delta t}[/tex] ..............2
power = [tex]\frac{0.50 \times 10^{-3}}{8.33 \times 10^{-10}}[/tex]
power = 600000 W
and
intensity of the microwave beam is
intensity = power output ÷ base area ..............2
intensity = [tex]\frac{600000}{30 \times 30 \times 10^{-4}}[/tex]
intensity = 6666666.66 W/m²
and
electric field amplitude is
as we know intensity I = [tex]\frac{E^2}{c \mu o}[/tex] ...............3
[tex]E(rms) = \sqrt{Ic\ \mu o} \\E(rms) = \sqrt{6666666.66 \times 3 \times 10^{8} \times 4 \pi \times 10^{-7} }[/tex]
E(rms) = 50119.87 N/m
and we know
[tex]E(rms) = \frac{Em}{\sqrt{2}}\\50119.87 = \frac{Em}{\sqrt{2}}[/tex]
Em = 70880.18 N/m
and
force on the base due to the radiation is by the radiation pressure
[tex]Pr = \frac{l}{c}[/tex] ..................4
[tex]\frac{F}{A} = \frac{l}{c}[/tex]
so
F = [tex]\frac{6666666.66 \times 900 \times 10^{-4}}{3\times 10^8}[/tex]
F = 2 × [tex]10^{-3}[/tex] N
