Question

The electric field intensity of a plane wave traveling in free space is given by the following expression

→E(x,t)=ay24πcos(ωt−k0x)(V/m)

In this field, consider a square area 10 cm × 10 cm on a plane x + y = 1. The total time-averaged power (in mW) passing through the square area is _____

Answer 1

The total time-averaged power passing through the square area is 0 mW.

Step-by-step explanation:

To find the total time-averaged power passing through the square area, we need to calculate the time average of the expression for electric field intensity within the given area. Let's integrate the expression with respect to x and y over the given area:

∫∫E(x, t) dxdy = ∫∫ay/(24π)cos(ωt−k0x) dxdy

Next, we need to find the time average of the cosine function over one complete cycle:

∫[0,2π]cos(ωt−k0x) dt = 0

Since the time average of the cosine function over one complete cycle is 0, the total time-averaged power passing through the square area is 0 mW.