A flat, square surface with side length 3.40 cm is in the xy-plane at z = 0. Calculate the magnitude of the flux through this surface produced by a magnetic field B=(0.200 T)i+(0.300 T)j-(0.500 T)k .

Video transcript

Hey everyone. So this problem is working with magnetic flux. Let's see what they are giving us and what they're asking for us. We have the center of mass of a rectangular sheet. Were given these dimensions here and it's placed in the horizontal plane at the origin. They give us a magnetic field in that region with X, Y and Z. Or I. J. And K. Components. And they asked the magnitude of the magnetic flux through the sheet. So the first thing we need to do here is recall the equation for magnetic flux. So magnetic flux or by is given as B. A. Times cosine of Theta. So let's take these terms one by one B is the magnitude of the magnetic field. And so we know that we have a horizontal, the sheet is on a horizontal plane. The sheet is in the xy direction. The magnetic field is perpendicular to that. So in this case the only component of the magnetic field that matters is this Z component. So the magnitude of the magnetic field is minus 3.0. Tesla A. Is just the area of the sheet. Um And so that's simple. It's recall that's length times width went for the area of a rectangle. And so I'm just going to rewrite these values in terms of meters. So we have 0.045 m times 0.035 m. And that comes out to 1.57, 5 times 10 to the negative three m squared. And then data. Alright. So what's data here? So Theta is the angle between a vector that is perpendicular to the area of the field, To the area of the sheets and the magnetic field. So let's just draw this out here. So we have the sheet, we have this perpendicular vector. And then we know that our magnetic field is -3 in the Z direction. So the angle between these two Is 180°. Alright, so our theta is 180°. The Kassian of 180° is one. That term just kind of goes away. So from there we can plug and chug to solve four. Our magnetic flux. So we have negative three Tesla times 1.575 times 10 to the negative three m square for our area. And our magnetic flux comes out to negative 4.73 times 10 to the -3 Tesla meters squared. The last little part of this. We need to realize that it's asking us for the magnitude of the magnetic flux, which simply means the absolute value. Recall that Tesla meters squared is the same as a weber different units the unit for magnetic flux. And so the magnitude of our magnetic flux is 4.73 times 10 to the negative three Webbers. And if then we go and look at our possible answers that is answer B. So B is the correct choice for this problem. That's all we have for this one. We'll see you in the next video.