Figure 16-28 shows a prism-shaped object that is 40.0 cm...

Figure $16-28$ shows a prism-shaped object that is $40.0 \mathrm{~cm}$ high, $30.0$ $\mathrm{cm}$ deep, and $80.0 \mathrm{~cm}$ long. The prism is immersed in a uniform electric field of $500 \mathrm{~N} / \mathrm{C}$ directed parallel to the $x$ axis. (a) Calculate the electric flux out of each of its five faces and (b) the net electric flux out of the entire closed surface. (c) If in addition to the given electric field the prism also enclosed a point charge of $-2.00 \mu \mathrm{C}$, qualitatively how would your answers above change, if at all?

Transcript

00:01 All right, so let's say we have a prism that has a shape, sort of like what i've drawn here.

00:07 Let's draw it like that.

00:09 And it has a height of 40 centimeters and a length or a depth of 30 centimeters.

00:23 So this is not really going to look like it's drawn to scale.

00:27 And it has a length of 80 centimeters.

00:32 So that's this distance.

00:34 And it's subject to an electric field everywhere that is 500 newtons per kulum directed to the x -axis.

00:45 So we'll say like this, kind of.

00:50 And this is 500 newtons per kulum.

00:53 And we want to calculate the electric flux out of the entire closed.

00:58 Surface.

00:59 So there are only two surfaces that we really have to worry about because the electric field is parallel to the, or perpendicular to the normal vector of the other surfaces.

01:08 So there's no contribution.

01:12 So if we draw this from the side, we're going to have our electric field like this.

01:17 Right.

01:18 And so the flux out of this back surface, we'll just call this phi b, is going to be our electric field strength 500 newtons per kulum times the area of this region.

01:32 So it's going to be 40 centimeters times 80 centimeters or 0 .4 times 0 .8 times 500.

01:41 So this is point, sorry, times 0 .32 square meters.

01:47 But there's a negative sign because the normal vector of that face points this way.

01:52 And so it'll be negative 160.

01:54 And the units, we can just say, are newton meter squared per kouon.

02:02 And then out of the front face, we'll call this phi f...