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190) Problem 2: pomt chaige pYIoned em cuh SOwM Ile mgure Otheexpertta.com 50"e Part (a) What the electric flux though the side (the top) ofthe cube? 0co) GaleSumnan [ktucfint Cuacma nia 0(240) 04820) Yao) 0MJo' Sulutuft lunt Aenipl nlIMJIE (uuper ncleniptl bubau Iene up' Wlahale Henmm Icliliuiiuy FaaIlae Hleanti Jerlt Sueran Wa Ahe elecUric Ilux Ilugh Ilte sulc Uthe Uton} ot the cub"



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12.6. The cube in Fig. 22.32 has sides of length $L=10.0 \mathrm{cm} .$ The electric field is uniform, has magnitude $E=4.00 \times 10^{5} \mathrm{N} / \mathrm{C}$ , and is parallel to the $x y$ -plane at an angle of $36.9^{\circ}$ measured from the $+x$ -axis toward the $+y$ -axis. (a) What is the electric fiux through each of the six cube faces $S_{1}, S_{2}, S_{3}, S_{4}, S_{5},$ and $S_{6} ?(b)$ What is the total electric flux through all faces of the cube?

So that or what? Here The figure this much is showing that had a length of 1.4 m. So that this is you and has a length of 1.4 would you like? And what more information we have Is that a certain figure and face in an xy plane? Right xy plane case in xy plane. Xy plane. Okay. So that's likely to have a pipe. Here's an excerpt uh energetic obviously and a couple of blocks from the right chest. If the uniform in formula to fill in the northern sparkle um is given by six hi minus two J. And six military. I plus four K. What is the 12 blocks to the two of these? Like, So basically we know that in the first past, since then we have given the like the CUBA were here. And this is lying in that way since that. Uh let's see. You see the X. So this this in the X. This is why this is there. You see the language, let me tell you again. You see the X. Y. And did. So basically the case is lying in the xy plane. So basically the first part they have to collect will do nothing. But yeah, I doubt doubt. Yeah, so you know that for the right yes, for the right face. Yeah, after will be in the uh writes this. Yes, there will be in the cap in the cab. Okay, so what drives this one deputy in the cab that was electric electric flux fire will be you doubting. So he is in the direction of six I six I yeah, one point front of all for 1.96 into jakob. So I into adulthood there that will be zero. Obviously ended with the next part. We need to find it is my studio. So Plus now we do nothing about -2 years Cap about 1.96 Jacob. All right. Uh how you doing? Mhm mm. No, actually, yeah, So it will be innovative and that will be, I think about minus of uh 12 9 Uh three. And it will be that will be mhm. A new 10 vampire meter square. Okay. Now in the next part We have electric field that it ministry at plus 40. Right? So perhaps now will do nothing but -3. I plus four K. In 2 1.96 checkups. Again, I doubt there will video and cable video. So it will be again. Now the flexible surfaces, the little flock through income. So basically not going to find a girl. So we know that since it is a close up that was products lots entering and leaving out will be the same. So that means uh anything revisiting and living out in the negative so that in certain floods that will be just go, okay, thank you.

For this problem. On the topic of gases law. We are shown a cube with excellent 1.4 m and it is oriented as shown in the region of a uniform electric field. We want to find the electric flux through the right face. If the electric field is given by six I had Newton speculum two minus two. J. Had newton curriculum and then minus three. I had plus four K. Had newton speculum. We then want to find the total flux through the cube for each field. Hey now we'll use the flux phi is equal to the electric field. E dotted with the area vector A. Where the area of actor A. Is equal to A. In the J. Direction, which is 1.4 m2. Mhm. Okay. In the jihad direction. So for part A we have the flux phi to be six Newtons. Cool. Um I had started with one 0.4 meters squared jihad and you know, I had Jihad is equal to zero. Yeah. Mhm. Next for B we have the flux phi to be minus to Newton's McCullum. Jihad Started with the area 1.4 m squared. Jihad. Which gives the flux to B -3 92 Newton meters squared, but cool on through the right face. Yeah. Yeah, for part C the flux phi is equal to minus three. Newton's cool. Um I had plus 400 Newton's cool. Um K hat Dotted with 1.4 m squared Jihad and I had dot jihad as well as K had jihad about equal to zero. So the flux through the right phases equal to zero. And lastly we want to find the total flux through the cube for each of these fields. Now we know that the total flux of a uniform field through a closed surface is always zero.

This is checked or twenty two problems. Six from the Sears and Saman Skis University physics textbook. The Cuban figure E twenty two point six has sides of length. L equals ten point zero centimeters. Electric field is uniform with magnitude equals four point zero zero times ten cube noons per column and his parallel to the X Y plane at an angle of fifty three point one degrees, measured from the positive X axis toward the positive waxes. What is the electric flux to each of the six cute faces? S one as to as three Asfour as five and six. And what is the total electric flux to all faces of the Cube? All right. The first thing I've done is I've sketched out the Cuba, as shown in the Figure Es Juan is the left side, as two is the top as three is This right side, as for is the bottom of the Cube s five is the front of the cube, and then s six, which is the hardest one to represent, is the very back of the queue I've also drawn the electric field is not shown in the diagram, but I've shown that in Blue Electric field is parallel to the X Y plain, as shown. So we imagine it going parallel to the plain form by the X and Y axes. But it's at an angle of fifty three point one degrees, measured from the positive X axis. Going toward that, the positive wax it so we can see that angle, which I have shown a state A is fifty three point one degrees. So that's the angle, as the electric field is going standing out from the Z axis those uniforms of the Cube. So I've just sketched a couple of the electric fuel lines for illustrative purposes. So our basic definition for electric flux is what we're going to use her. All six sides. Electric flux is simply the Electra revealed, multiplied by the area of each side times. A co sign of this angle five and five is the angle that is between the normal to the surface and the direction of the electric field. So we need to just figure out what fires, because that's what's going to change for each of the sides. So with this basic definition, well, we know the electric field. In each case, is uniforms four point zero zero times ten Cube Newtons per column, and we know the area of each side. It's a cube, so it's just length times length. So the area is elsewhere along us to rewrite electric flux as e l swear times the co sign of fun. So we just need to repeat this calculation right here for each and every one of the sides. I'm not going to write this out for each and everyone, because it's just plugging it. He Dr Field is always this value that were given and l is always ten centimeters and make sure to convert two meters from ten centimeters each time that you are computing this calculation right here. So we always want to make sure we're in standard units, so we will just rear. We write this basic basic one here, and that's the same thing as point one zero meters. So make sure to use this value each time since we're working in Newton's and cool ums, so everything needs to be in standard units. Alright, so elsewhere it is the same for each one, so the only thing that will change is by for each one for surface s one, which is on the left side. Well, that FIEs our angle here fifty three point one degrees because that's how far we are. But the normal to s one is pointing out the negative wide direction. So that's ninety degrees from the X axis. So we have fifty three point one minus ninety degrees to get the angle five, and that gives us the electric flux. Then on side one is negative. Thirty two new meter square, two per cooler for side as to which is at the top, the angle between the electric field and the normal to the surface, which is in the positive zy direction. Well, that angle is ninety degrees, but the co sign of ninety degrees zero. So there's no electric flux going through. Truth s too. And it's going to be the same thing for s for a CZ. Well, as for is the bottom one exact same calculation. The angle is ninety degrees because it's going straight down the negative Z direction. So again, the flux us for is zero for Sy s three, which is on the right side here, going street. In this case, it's flipped from s one those ninety, ninety degrees minus fifty three point one degrees. So we use that that angle Plug that in for five to give a positive thirty two Newton meter square to purr cool. And then for as five and six, the front and the back for s five, which is going in the positive ex direction. The angle between the normal to the surface s five. That normal is along the extraction. So the electric field is at an angle of fifty three point one degrees angle that were given. So we plugged that angle and for five to get the answer of twenty for Newton meter squared per column and then as six, Well, we go in the negative X direction because we're going out the back of the Cube. So that's starting at one hundred eighty degrees minus one hundred minus fifty three point one degrees. Which gives us the negative answer that we've got an S five. So we get a negative twenty for Newton meter squared her Kula. So these values then give you the total flux going through each and every one of the sides. Part B is very simple. It's just what is the total electric flux through all faces of the Cube. Couple ways you could do this first. You could just know. Know that the total flux do that you must be zero, because any flux that enters that you must also lead. So it doesn't matter what side it comes through, the total sum of all electric flux. Since the electric field is from outside the cube, then the total electric flux must be zero. Anything that goes in must come out or you could also calculate just add together. The electric flux is for all six surfaces. So we have negative thirty two plus zero plus thirty two plus zero plus twenty four plus negative twenty four and that total Some gives us a zero as well. If you wanted to do so mathematically. So total answer, then, is just zero for the total flux. There is no total flux because everything it remains balanced out

A que off sideline. 10 centimeters is exposed to an electric field. That's fair health to the ex wife thing. It's also at an angle from the positive X axis of 53.1 degrees for so I access a scene in this figure on the right to find the electric flux that goes through east side of the Cube. You want to take the surface interval off the lucky feel that interaction the incremental area or just the top on it between the liquor field and that area. You can also write this as perpendicular portion of that liquid field with respect to that area, or even taking on the surface of the magnitude of electric field and the magnitude of the incremental area I was applying like co sign of data. Which data is the angle normal to the area with respect to the locker field now looking at East Side separately? The first thing to note out is that for aside to floor, that is for the bottom and top services. Those are completely parallel to the electric field being there's no perpendicular compliant between the two, so those two should be zero. Since there's no area that captures them now, looking at the other war, Syed's case records with me outside six Side six is oriented opposite to the incoming electric field. The normal of it is in the opposite direction, so that should give us a negative force, since electric field doesn't depend on area and you wait the interval. Just be a Saturday multiplication. So solving for the flux and using an angle of 53.1 with me negative times the magnitude of the electric field or have sent to three years before times. Incremental area. 0.1 square meters. Where. Times co sign of the angle. 53.1 degrees. And that gives us negative running for new hands. Meters squared her full now looking, get the other side on the front side side. Five. It's identical in size six set. It looks the other way, so it will give us 24. Yes, you swear her cool. Finally, for the other two sides, that's two side one that is also facing opposite to electric clear bites. But in this case, we don't even ships in 3.1. You hear about this angle that's perpendicular to the incremental area, which is 90 in minus 53.1 degrees. Real value. Eating that again. Influx of one that gives us negative four times. 10 through the three moons for sending me for cooler, 0.1 square meters away. Times worse I of 90 by 1963.1. And that gives us an answer, maybe of 32. Newt is meters square hole, and once again, fuck's four side three will be the opposite of side one. Well, you just 32 minutes years before adding this all together, the Netflix will just be zero since his 30 to minus 32 plus 20 for minus 24 then two zeros.


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