What is the total flux through the two surfaces depicted in the following figure? Note that surface 1 has an area of 50 cm 2 and surface 2 has an area of 100 cm 2 , and E = 500 N/C.

Alright, guys, let's take a look at another practice problem. We have to calculate what the total amount of flux is through these two surfaces. So you've got service one service to we're just gonna calculate the flux is for both of them and put them together. Now we're not told any directions in terms of, like, the normal vectors, So we're just gonna go ahead and assume that everything in this problem is going to be positive. So first things first. If we wanted to calculate the flux for the first surface we have the electric field, which, by the way, is equal to 500 Newtons per Coolum. And it's constant times the area of that first surface times the cosine of the angle between those two things. So we've got the electric field. It's just 500 Now. The area we're told of surface one is equal to 50 centimeters squared, so 50 centimeters squared. Just be careful is not the same thing as 0.50 m squared. You actually have to do the conversion twice. So 50 centimeters squared actually turns out to be 500.5 m per centimeters. Squared eso anyway, that's the area so that we're just gonna plug in 0.5 Now, we just have to figure out the cosine of the angle between the electric field and the normal. So first things first, we actually have to draw that normal. So I'm gonna just draw that sort of perpendicular line segment right here. So that means that the angle between the perpendicular and the electric field is actually going to be this one right here. But if you take a look, we actually have this angle right here between that electric field and the A t least the vertical line here, which is actually gonna be parallel to this. So that means that this is the angle that we're working with, at least for this top surface right here. So that means that the co sign is we're gonna take the coastline of 40 degrees. And if you go ahead and work this out, where you're gonna get is you're gonna get 1.92 that's gonna be Newton meters squared per cool. Um, so that's the electric flux across that first surface. Now we have to basically repeat the same process over here for flux, too. So this is the second surface that's gonna be times the area of the second surface times the co sign of this angle right here. So first I have to draw the perpendicular, which is gonna be right over here. And now the angle that I'm interested is, if I sort of extend this electric fuel line out like this, then the angle that I'm interested is the one between the electric fields and the normal the perpendicular of that surface. And so these are opposite angles right here. But this does not represent 40 degrees. Instead, we actually have to sort of do some geometry a little bit. So this angle right here is actually going to be, uh, 90 degrees minus this 40 degrees. So, in other words, we're not gonna use 40. So that's the wrong angle. What we are actually going to use is 50 degrees, so this 50 degrees represents the angle between the electric field and normal off this surface right here. So we now we have to do co sign of 50 degrees on day, so that's gonna be Let's see, we've got 500 then we've got the area of the second surface, which we're told is 100 centimeters squared. So that's gonna be 1000.1 just because the same conversion that we did let over here and then we've got co sign of 50 and that's just equals, Let's see, I've got 3 21 and that's gonna be, uh, Newton meters squared curriculum. So just to finish things off, the total flux is gonna be the flux between both of these two surfaces. So this was 3.21. This was 1 92. So I just go ahead and add those things together. We've got three or 1.92 plus 3.21 equals 5. Newton meters squared per Coolum. That is our final answer for the total of electric flux. All right, let me know if anything any part of this sort of process confuse you. Just drop me a comment if you want to explain anything and I'll see you guys in the next one

Struggling with Physics with Algebra?

What is the total flux through the two surfaces depicted in the following figure? Note that surface 1 has an area of 50 cm2 and surface 2 has an area of 100 cm2, and E = 500 N/C.

Watch next

What is the total flux through the two surfaces depicted in the following figure? Note that surface 1 has an area of 50 cm² and surface 2 has an area of 100 cm², and E = 500 N/C.