Alright, folks. So let's take a look at this example problem here. We have a radio tower that's emitting some kind of radio signal with an average power output of 50,000 watts. In other words, that's our P or P average, which equals 50,000. This radio tower emits equally in a hemisphere above Earth's surface. Basically, what happens is if you could imagine that the ground is here, the signals can't penetrate through the ground, so it sort of radiates equally in a hemisphere, not a perfect sphere.
Now, we want to calculate the intensity that's detected by a satellite passing overhead at a height of 100 kilometers. From the radio tower up to this satellite, this is going to be my H, which equals 100 kilometers. So let's start with that first part, which is the intensity. To calculate the intensity, we just have this one big long expression to do this, which is just power divided by area. In this problem, we have no information about Emax, ERMS, Bmax, or BRMS, or anything like that. So this whole problem can be solved just by using I = P/A. Right?
We have the power, and we need to calculate the area. The area of a hemisphere is really just equal to one-half of the area of an actual sphere, which is 1/2 of 4πr2. So this means the area of a hemisphere that we're going to plug into our equation is actually 2πr2. The radius is just the distance between the radio tower and the satellite, which is
Now, moving on to the second part, it asks us to calculate the power that's received by the satellite's circular radio antenna with a radius of 0.5 meters. The antenna captures signals with an intensity
So, just to recap, in part A, we used the power of the radio tower and the area over which it broadcasts to figure out the intensity at a specific point. In part B, we reversed the equation to figure out the power received by a radio dish of a different size. Let me know if you have any questions in the comments, and I'll see you in the next video.