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 magnitude force does the microwave beam exert on the base of the oven? (c = 3.00 × 10⁸ m/s, μ₀= 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 1.6 µN B) 2.0 µN C) 2.5 µN D) 3.0 µN E) 3.5 µN

Question

Quizplus · Accepted Answer

First, we need to find the power of the microwave beam:

$P = \frac{E}{t} = \frac{0.50	imes10^{-6} J}{1	ext{ cycle}} = 0.50	imes10^{-6} W$

The electric field strength can be calculated using:

$P = \frac{\epsilon_0}{2}E_0^2cA$

where $\epsilon_0$ is the electric constant, $E_0$ is the electric field strength, $c$ is the speed of light, and $A$ is the area of the upper surface of the cavity. Solving for $E_0$:

$E_0 = \sqrt{\frac{2P}{\epsilon_0 c A}} = 304.79 V/m$

The force exerted on the base of the oven can be calculated using:

$F = \frac{\epsilon_0}{2}E_0^2A = 1.25	imes10^{-6} N$

Since the force is acting directly downward, the magnitude is simply:

$|F| = 1.25	imes10^{-6} N = 2.0\ \mu N$

Therefore, the best choice is B.

A Microwave Oven Operates with Sinusoidal Microwaves at a Frequency