It is proposed to store 1.00 kW•h = 3.60 * 10^6 J of electrical energy in a uniform magnetic field with magnitude 0.600 T. (b) If instead this amount of energy is to be stored in a volume (in vacuum) equivalent to a cube 40.0 cm on a side, what magnetic field is required?

Video transcript

Welcome back, everybody. We are making observations about a television set and we are told that it consumes 75 watts Per hour and we are told that this is equivalent to 2. times 10 to the fifth jewels of electrical energy. Now, we want to store this electrical energy in a evacuated cylindrical space. We're told that it has a radius of 20 cm in a height of 30 cm. And we are tasked with finding what is going to be the magnitude of the required magnetic field for this. Well, we know that electrical energy per volume is just equal to the magnetic field squared divided by two times a constant mu Not. Now, what I'm gonna do is I'm gonna multiply both sides by two mu. Not, do you not? You'll see that these terms cancel out on the right in order to get rid of the power, I'll just take the square root of both sides. And you'll see that that gets rid of the power on our magnetic field magnitude of our magnetic field. So we are left with B is equal to the square root of two mu not times our electrical energy divided by the volume of our cylindrical space. We know the volume for a cylinder is pi R squared H. So we'll just plug that in right here. So let's go ahead and find the magnitude of our magnetic field. Here. We have that B is equal to the square root. Want to make this a long radical of two times mu not which is four pi times 10 to the negative seventh times are electrical energy of 2.7 times 10 to the fifth jules. This is all divided by our volume of pi times R radius which is 20 centimeters, but we need it in meters. So we're multiply by 10 to the negative two squared times our height of centimeters. But once again, we need it in meters. So we're also gonna multiply this by 10 to the negative two. And when you multiply this all out, we get a magnitude of the magnetic field to be 4.2 for Tesla's corresponding to our final answer. Choice of B. Thank you all so much for watching. Hope this video helped see you all next one.