An open plastic soda bottle with an opening diameter of 2.5 cm is placed on a table. A uniform 1.75-T magnetic field directed upward and oriented 25° from vertical encompasses the bottle. What is the total magnetic flux through the plastic of the soda bottle?

Video transcript

Hey everyone. So this problem is working with magnetic flux, let's see what they give us and what they're asking for. So we know that there is a uniform magnetic field of a certain strength, it is directed at an angle they give us from the Z directions. That's important. Um We have a water picture that's made out of glass and it has a circular plastic top. So we have two different materials here and then they give us the top radius. We know the picture with the glass or the picture with the plastic top lies within the magnetic field and it's on top of a horizontal table. So we need to determine the total magnetic flux that's passing through the picture glass. So the first thing we need to do here is recognize that we have two different materials. So the total flux is going to be the flux of the glass plus the flux of the plastic. We can also recall that the total flux and a closed surface is zero. We know it's closed. We have a top on top of the picture and so the total The magnitude of the total flux is going to be zero. So we can rewrite this as the flux of the glass is equal to minus the flux of the picture. Let's recall that the equation for flux is given as B. A. Times Kassian data. Now they're asking us for the flux of the glass, but we really have no way of calculating the area of the glass picture through this relationship though. We can calculate the area of the plastic top and then find the flux of the plastic top, which then gives us the flux of the glass picture. So let's calculate the flux through the plastic top. We have the magnetic field, the area of the plastic top and the cosine of theta. So take this term by term. The magnetic field strength is given as 1.5 1.15 Tesla. The area of the top, what's called? The area of the circle is just pi R squared. So I'm going to rewrite our in terms of meters that 0.7 m squared, that comes out to 1.54 times to the -2 m squared. And then uh See our data was given to us in the equation as 37°. So from here we can just plug all of that into our equation. And we come out with 1.4, 1 times 10 to the -2 Levers, going back up to this original equation. They're asking us for the flux through the glass. We know that's the opposite of the flux through the plastic top. And so the flux through the glass picture is minus 1.41 times 10 to the negative second Weber's. We go and look up our potential answers and that aligns with answer a that's all we have for this problem. We'll see you in the next video