Answer :
Answer:
1584.6 V/m
Explanation:
The energy density (the energy per unit volume) for an electromagnetic wave is given by the equation
[tex]w=\epsilon_0 E^2[/tex]
where
[tex]\epsilon_0 = 8.85\cdot 10^{-12} C^2/Nm^2[/tex] is the vacuum permittivity
E is the amplitude of the electric field of the wave
At the same time, the energy density can be written as
[tex]w=\frac{U}{V}[/tex]
where
U is the total energy of the wave
V is the volume considered
So the first equation can be written as
[tex]U=\epsilon_0 V E^2[/tex]
Or
[tex]E=\sqrt{\frac{U}{\epsilon_0 V}}[/tex]
In this problem:
[tex]U=0.50 \mu J = 0.50\cdot 10^{-6} J[/tex] is the total energy of the microwave
The volume considered is the volume of the cavity, so:
[tex]V=0.25 m \cdot 0.30 m \cdot 0.30 m = 0.0225 m^3[/tex]
Therefore, the amplitude of the electric field is:
[tex]E=\sqrt{\frac{0.50\cdot 10^{-6}}{(8.85\cdot 10^{-12})(0.0225)}}=1584.6 V/m[/tex]