Hello, everyone and this problem. We're told that there is a broadcasting station for television show that is a meeting radio signals over a hemisphere, and you're asked to find various quantities about these waves, such as the radiation pressure it exerts on a completely reflecting home five kilometers away from the station. So we have the distance to the home is five kilometers, where five times 10 33 m speed of flight is three times and 3 m per second. As usual, the electric primitive ITI is 8.85 times in three minus 12 for aspirin meters. The power that the station emits debate with is 316 times 23 watts were 316 kilobytes. And because it's free because it's radiating signal over hemisphere, not the entire sphere, you have that the area over which this power distribute is distributed is a half times four by R squared. So the first thing we are as to find is the pressure to radiation pressure provided that the home is a completely reflecting service. Okay, so for completely respectful service service, we have the radiation. Pressure is two times the intensity divided by the speed of flight. Okay, but we're not giving the intensity. So how do we find the intensity? Well, the intensity is the power over the area. So it's the It's the energy transmitted per unit, time per unit area. And so we're giving the area as well because we're no the distance. So we could just work out I two b p over a half times four pi r squared. I'm not going to give a value for this. We can just leave it in terms of symbols and just work with that and simplify everything and put into values at the very end. Okay, so given that this just the intensity and this is the radiation pressure that we have to calculate, we can combine the two to find that the radiation pressure is two times p over two pi r squared, oversee So here to choose, cancel and then we can multiply this one oversee into the pi r squared. Let me have that. The radiation pressure is the power divided by pi r squared times the speed of flight and putting in the values from your bob Here we find that the radiation pressure is 1.34 times and threw minus 11. Paschal's okay, so that's the answer to part A. On the next board were asked to find the electric and magnetic field amplitude. So we know that there is a relationship between these amplitude is that says that the maximum electric field amplitude is equal to see times or the speed of light times deep magnetic field amplitude. So given this relationship, it's actually enough to work out just what IMAX is. And in terms of IMAX, we know that the intensity is given by ah half times Epsilon zero has the speed of flight times imax squared Serie arranging this equation over here for IMAX find that imax the square root of two times I divided by absolute zero times. See? And then again, we use our trusty formula from up here for the intensity. So I just use this I over here again Choose cancel. We're gonna have that Thea Electric field amplitude is squaring off the power divided by pi r squared times. Absolutely. You can see putting it all the values we find that this is equal to 1.23 ball square meters, okay, and then to find a magnetic field amplitude. We just simply divide this value over here by sea. And we get that The magnetic field amplitude is 4.10 times 10 to the minus nine. Tesla's Okay, easy enough. And then, in part, Sceviour has to find what the average energy density toe wave carries is And so that is given by, you know, the energy density. You is absolute zero times e uh, he squared, but the M X squared. But because we're doing an averaging, you're averaging the oscillations over time. And so we pick up a factor of half. So you bar the average energy density is a half times episode zero times um, X squared and that works have to be equal to 6.70 times 10 to the minus 12 jewels for meters cube. Okay. And then in the last party were asked to find, Whereas what percentage off the of this energy density is carried by the electric and the magnetic fields, and that is just 50 50. So half of the energy density is carried by the, uh half. The energy density is carried by the electric grave or the electric field and the other half is carried by them in that field. And the reason for this is that we're doing it everything. So obviously, if you're calculating the energy density, strictly speaking, you're going to be finding that the energy density also oscillates, just as do the electric and magnetic fields. But it's always gonna be true that they carry half off the total energy debt.