Estimating the peak electric field

[patelpalak]

Homework Statement

Find the peak electric field inside a 690 W microwave oven under the simplifying approximation that the microwaves propagate as a plane wave through the oven 's
775 cm^2 cross-sectional area.

The Attempt at a Solution

ave, intensity (s) = ave power (p)/ 4*pie*r^2

so in this formula i substituted ave.S=E^2/ 2* 4*pie*10^-7 *3*10^8

and i got E^2 = (p)(2)(4*pie*10^-7)(3*10^8)/ (4*pie) (r^2)

and when i plug in all the #s
its E^2 = (690 W) (2)( 4*3.14*10^-7 N/m^2) (3*10^8 m/s)/ (4*3.14)(7.75 m^2)

= 53.419 V/m
i get this answer
am i mistaking somwhere?
plez help to get me a right answer...thanx!

 

[anathema]

I would like to commend you for your attempt at solving this problem. Your approach is correct and the formula you used is appropriate for calculating the peak electric field. However, there are a few corrections that need to be made in your calculations.

Firstly, the units for power should be in watts (W) and not newton per square meter (N/m^2). So, the correct value for power should be 690 W.

Secondly, the value for permeability of free space (μ0) is 4π × 10^-7 N/A^2 and not 4π × 3.14 × 10^-7 N/m^2. Therefore, the correct value for the peak electric field would be:

E^2 = (690 W) × (2) × (4π × 10^-7 N/A^2) × (3 × 10^8 m/s) / (4π) × (7.75 m^2)

= 2.6 × 10^-4 N/C

= 16.1 V/m

I hope this helps you to arrive at the correct answer. Keep up the good work!

 

[nlightner]

I would like to commend you for your attempt at a solution and for using the appropriate equations to solve for the peak electric field. However, there are a few things to consider in your calculations. First, make sure to use consistent units throughout your calculations. In your attempt, you have used both meters and centimeters, which can lead to errors in your final answer. Also, the formula you have used assumes that the microwaves are propagating through free space, not through the oven's cross-sectional area. You may need to consider the dielectric properties of the oven's interior and the reflection and absorption of the microwaves in your calculations. Additionally, it would be helpful to provide some context or background information on the problem, such as the frequency of the microwaves and the dielectric constant of the oven's interior. Overall, your approach is a good start, but further considerations and clarifications are needed to arrive at a more accurate answer.