A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz.The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm.Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base.The base is lined with a material that completely absorbs microwave energy.The total microwave energy content of the cavity is 0.50 µJ.What is the amplitude of the electric field? (c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A)1600 V/m B)1900 V/m C)2200 V/m D)2500 V/m E)2800 V/m

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Quizplus · Accepted Answer

The energy stored in an electromagnetic wave is given by the equation $U = \frac{1}{2} \epsilon_0 E^2 V$, where $U$ is the energy, $\epsilon_0$ is the permittivity of free space, $E$ is the electric field amplitude, and $V$ is the volume of the cavity. Rearranging for $E$, we get $E = \sqrt{\frac{2U}{\epsilon_0 V}}$. The volume $V = 0.25 m \times 0.30 m \times 0.30 m = 0.0225 m^3$, and given $U = 0.50 \times 10^{-6} J$ and $\epsilon_0 = 8.85 \times 10^{-12} F/m$, substituting these values gives $E \approx 2200 V/m$.

A Microwave Oven Operates with Sinusoidal Microwaves at a Frequency