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Chapter 29: Problem 30

Estimate the peak electric field inside a 1.1 -k \(\mathrm{W}\) microwave oven under the simplifying approximation that the microwaves propagate as a plane wave through the oven's \(750-\mathrm{cm}^{2}\) cross-sectional area.

Short Answer

Expert verified
The estimated peak electric field inside the microwave oven is approximately 434 V/m.

Step by step solution

01

Convert the Power into Watts

First, convert the power from kilowatts to watts. 1 kW equals 1,000 W, thus \(P = 1.1 kW = 1100 W\)
02

Convert the Area into Square Meters

Next, convert the area from square centimeters to square meters. 1 sq meter equals \(10^{4}\) square centimeters, hence \(A = 750 cm^{2} = 0.075 m^{2}\)
03

Calculate the Intensity

Using the formula for intensity \(I = \frac{P}{A}\), substitute the values for power and area calculated in steps 1 and 2 to find the intensity \(I = \frac{1100 W}{0.075 m^{2}} = 14666.67 W/m^{2}\)
04

Solve for Electric Field

Rearrange the intensity formula to solve for \(E\) as \(E^{2} = 2I渭_{0}\). Substitute \(I = 14666.67 W/m^{2}\) and \(渭_{0} = 4蟺 x 10^{-7} T m/A\) to calculate \(E^{2}\). After finding \(E^{2}\), take the square root to find \(E\)
05

Compute the Final Value

Perform the calculation from Step 4 and this will present the estimated peak electric field inside the microwave oven, \(E\)

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