A circular area with a radius of 6.50 cm lies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.230 T (b) at an angle of 53.1° from the +z-direction?

Video transcript

Hey everyone. So this problem is working with magnetic flux, let's see what they give us and what they're asking from us. We have around loop of a given radius. It's placed on a horizontal table, solenoid produces a uniform magnetic field of a given strength. And the magnetic field is directed at an angle below this angle degrees below the horizontal. And we are asked to determine the magnitude of the magnetic flux through this loop. So the first thing we need to do is recall our equation for magnitude of the magnetic flux that's given by phi equals B. A. Cosign data. So let's take this one term at a time. B is our magnetic field strength. And so that's zero given to us in the problem as 0.32. Tesla A. Is the area. And so that we did they give us the radius. We just need to recall the area is pi R squared. I'm gonna rewrite the radius here in terms of m. So that's .15 m Squared. And that gives us 7.07 times 10 the negative two m squared. And then Theta. So they actually give us a angle in the problem. It's 42 degrees. So it might be tempting to say, okay, data is 42 degrees but we need to remember that theta is the angle between a vector that is perpendicular to the area and the magnetic field. So let's draw our, you know, our we know we're working with a horizontal table and the line perpendicular to that would be here. The magnetic field is 42° below the horizontal. And this angle here is beta. This is the angle that we're looking for for the equation. And so that is just 90 -42, which is 48°. So that's the tricky part of this problem. But once we've got that figured out, then it's just plug and chug. So .32 Tesla times seven point oh seven times 10 to the negative two m squared times the cosign of 48 plug that into our calculators. And we are left with 1.51 times 10 to the minus to Weber's. Remember that a Tesla time is meters squared is a weber. So we get that unit and then we look at our potential answers and that aligns with choice. See, the answer to this problem is C. And that's all we have for this one. We'll see you in the next video