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A uniform line charge with linear density ^ lies along the Y-axis. What flux crosses a spherical surface cantered at the origin with r = RZRNJEOD. None f the aboveR...

Question

A uniform line charge with linear density ^ lies along the Y-axis. What flux crosses a spherical surface cantered at the origin with r = RZRNJEOD. None f the aboveRAEoNco

A uniform line charge with linear density ^ lies along the Y-axis. What flux crosses a spherical surface cantered at the origin with r = R ZRNJEO D. None f the above RAEo Nco



Answers

A uniform surface charge of density 8.0 $\mathrm{nC} / \mathrm{m}^{2}$ is distributed over
the entire $x y$ plane. What is the electric flux through a spherical
Gaussian surface centered on the origin and having a radius of 5.0 $\mathrm{cm} ?$

In this problem on the topic of electric fields and gases law, we have two point charges placed on the X axis. The first has a magnitude of plus Q. And is located at X. Is equal to a. The second has magnitude minus Q. And is located on the X. Axis at point X is equal to minus A. If we place a calcium surface surface with radius R. Is equal to a centered at the origin, we want to know the flux through the calcium surface. Now, by God's law, we have the total flux phi is equal to the charge enclosed within the Gaussian surface, divided by absolute or not, and the enclosed charge totally enclosed charge within our Gaussian surface is Q plus minus Q, which is zero. Since the total enclosed charges zero. The electric flux through our Gaussian surfaces also equal to zero. And so the answer here is a.

23.74. We have the sphere with a radius of six centimeters and the uniform charged density of 500 a cool homes per cubic meter. Now we consider a cubicle galaxy and surface centered. At this. The same center is our sphere. And if it's edulink this four centimeters or 14 centimeters, we want to find the electric flux through the surface. So if a part ay here, we can see that four centimeters the side length, it means each for genetic extends Buster minus two centimeters. From that access, it's well within the radius of our little sphere. And so, the, uh, the clothes charge is just going to be 500 nana pool alarms, cubic meter times the volume of of the sphere, which is 0.0 for leaders. You, this is 3.2. I'm standing to the negative 11th who owns. We know that our flux is equal. Few enclosed provided by epsilon, not which gives us 3.2 No. 3.62 Uh, I was 3.62 uh, Newton meters squared. Cool now for part B since it's ah what is this bigger than our sphere now aren't those charge is going to be row times the volume of this sphere. So the total charge on this fear is 4.5 times 10 to the negative 10th cool albums. Using their same equation, he finds that the flux will be 51.1 Newton meters squared cool with.

Okay, so this problem we have, ah, insulating solid this fear. So that's draw here. First of all, are sort of this fear, and we have to calculate the electric flux for ago ocean surface. When we inflate discussion, surface is starting in zero to infinity. Okay, so basically, that means that we have to calculate the electric flux in two different configurations. First of all, insight the insulated sphere. And second, we have to calculate outside the insulating. This year, let's begin with the inside guy ocean's surface. So first of all, going to calculate the electric feud electric flux. I'm sorry, Insight. So we know that the electric field flux is describe buzz, but but the charge inside the ocean surface divided by absolute zero. The first configuration when we have the Goshen surface inside the insulation sphere, the charge is not the entire charge. So is just hope the multiplies, the volume of the Gulshan surface divided by absolute zero. And as we know the charge, the density sorry can be described by the entire charge divided by the entire volume, plus the volume of the Goshen divided by absolute zero. To simplify this, remember that Fordham is just far divided by three by our cubic To simplify this, we can say that the flux inside the insulated sphere is going to be que that multiplies our cubic divided by absolute zero. A cubic when a he is the radios off the insulation sphere. So as we can see here, we have a power off our cubic inside. Now, the second situation, we have to calculate the electric flux outside the insulation sphere. In this configuration, we know that the electric flux stops. We know that the electric flux is just again the charge inside, divided by absolute zero. But this time the charge inside egg ocean surface is the entire charge, Q divided by absolute zero. So that's the electric flux. So, in part C of this problem, we have to make a blood off this flux. So this is Bart. See, uh, this is part B and this is sparked A Okay, So a lot of the flux. Alright, sport here. Your Y axis is going to be the electric flux. The X access is going to be the distance, the radios. So the flux until we get to the radios off the insulated sphere this is radios. A is going to be a cubic graphic. That means it's going to be something like this. Horrible. Okay, that goes until the value off. Uh Q divided by absolute zero. After that point, after a big ocean surface reaches the volume radius off the insulated sphere, the value stays constant and remains constant and shooting finish. So that's the flux. A lot of the flux to this problem, and that's all. Thanks for watching.

Problem based on calculation off electric flux by using goes through. Um, here it is, given a solid insulating his fear. Mm point. Yeah. Off radius aid having should charge distributed uniformly. So it's the radius is given a There is a question surface with sharing the center of the atmosphere off radius art. So this is given up bastions. Earpiece. We have to calculate flux a d function off part for hard to be less than a. We have to file the flux foot. All is greater than a and we have to plot flux versus our graph foot. Yeah, let us start solving it first part. Yeah. Judge enclosed. You can fight volume, charge density in the bottom bottom charges to his two upon four by three by a cube on bottom off the ocean surface 4.3 pipe, are you? So it is to me Q r Cuba, part a que hence flux Bill B. You enclosed upon absolutely not top tube our cube upon absolutely not a cube for value off art, Toby Equally less than eight. No second part. Oh, If r is greater than a then total charge and close will be equal to Cube. So flexibility, given close upon. Absolutely not. That is Cuba upon absolute? Not so. This is the Flux foot. All is greater than a wow. Now we have toe north a graph. Yeah, flux between and part and our zero flexibility zero. And it increases. With the increase off art on it becomes maximum at the surface that it remains constant, That's all. Thanks for watching it.


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