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For each homework question and lab report we will make a post, this will probably contain a few tips on what the problems are about and how to solve them. If you are stuck on something then instead of emailing us directly you should post a comment in reply to the relevant post. We will try to guide you through tough points and help you understand the problems and the concepts behind them.
Wednesday, September 1, 2010
Chapter 15, questions 10-12
These three questions are from SV8 sections 15.6, 15.8, and 15.9. The whole assignment is due on Tuesday, September 7th at 3:30 PM.
14 comments:
Anonymous
said...
I have a question on question 10 part A, I understand if the arrow is pointing away then the charge is positive and vise versa, but part A seems too easy and I want to make sure this is not a trick question before I put down negative over positive as the answer, any insights would be appreciated!
Textbook page 518 question 15.6 as part of the example 15.6:
I don't understand whether the spherical surface would be greater or less then on the same in erms of electrical flux. I think it would be greater just because there's so many more angles.
Discussion of question #10 - No trick - charge is proportional to the number of field lines. Actually, my recollection is that WA will accept either a positive or a negative answer of the correct magnitude. And did you get the news - no penalty for incorrect guesses?
In example 15.6, corners, angles, etc. make no difference. Gauss's law says the flux is proportional to the charge enclosed, which is zero. The problem with this blog is that it's not really possible to draw pictures. But notice that for each little area on the spherical surface on the x>0 side where the flux is posiive (outside of the sphere), there is an equal and opposite contribution from the x<0 side. So they cancel, and the total flux is zero.
On #12 I'm very confused! If I'm not mistaken, E = sigma / Eo...(electric field = sigma divided by 8.85e-12). The thing is, in the question a numerical value is tied in with sigma. And where do the distance values fit in? Please clarify...this problem has me stumped.
Think of sigma as being some specified charge density, whose numerical value you don't know, but you don't need. Think of one plate alone, say at z=0, first. If it had a charge density of, say, +5*sigma, the field above (z>0) the plate would be +2.5*sigma/epsilon0 (in the z direction), and for z<0, -2.5*sigma/epslion0. Note that WA wants you to fill in the numerical multiple of sigma/epsilon0, so if that were the problem, you would put 2.5 or -2.5 in the box. Now you have to superpose two planes of charge, like I did on the last slide of Sept. 2. The big difference being that in this problem, the two planes do not have the same numerical value. Does that clarify?
I still don't understand (I'm looking at the last slides from 9/2). Maybe I'm just missing it completely...but here's my reasoning:
E = Q / (Eo X 4pir^2) Then, I cancelled Q/4pir^2 because that's charge per unit area, which is given in two places in the problem (the negative sigma and the positive sigma). However, when I plug this in I get extreme numbers...nothing like the integers you just mentioned.
I think you're mixing up pieces for several different equations. E=ke * Q / r^2 = Q / (eps0*4pi*r^2) is the field a distance r from a point charge Q, or the field a distance r from the center of a sphere carrying total charge Q. But that doesn't depend on the charge density of the sphere. Anyway, in the last problem (is that what you're asking about?), we have an infinite sheet of charge, which has charge density sigma (Coul/m^2). The field from such a sheet of charge is sigma / (2*eps0), independent of the distance from the sheet. Does that help clarify?
Can someone explain multiple choice question 11 on page 524? I don't understand how the electrons on the ground's surface and the surface of your feet repel each other as the reason why the earth isn't capable of pulling you through the ground to the center of the earth.
Vito, I would say that there are a few steps missing in that answer (from SV8). Matter is made of atoms, which consist of electrons which exist in a cloud around positively charged nuclei (consisting of protons and neutrons), and for the most part these are electrically neutral - same number of electrons and protons. We'll look at this much more closely at the end of the course, but I hope it's familiar from chemistry you've taken. Atoms have a size, typically 1 or 2 x 10^-10 m. If you try to push two atoms too close together, the electrons that are out at the frontier of the atoms would begin to overlap and repel each other. We know that atoms that are not too close can form chemical bonds which attract them to one another, so that whole story is rather complicated. But that is the sense in which the repulsion between two objects in contact is due to the repulsion between electrons.
I'm still not getting number 12 on WA chapter 15. The worked out example in the book is not helping. I don't understand the reason for halving the charge (i.e. from 5 to 2.5 etc.) Help!
P.S. I have not received a single correct answer regarding number 12. It either tells me I have inputted the wrong sign, or that my answer is off by more then 100%. Help!
14 comments:
I have a question on question 10 part A, I understand if the arrow is pointing away then the charge is positive and vise versa, but part A seems too easy and I want to make sure this is not a trick question before I put down negative over positive as the answer, any insights would be appreciated!
It's not a trick question if your question looks like mine, its a question to make sure you understand that concept.
Its not a trick question.
Textbook page 518 question 15.6 as part of the example 15.6:
I don't understand whether the spherical surface would be greater or less then on the same in erms of electrical flux. I think it would be greater just because there's so many more angles.
Discussion of question #10 - No trick - charge is proportional to the number of field lines. Actually, my recollection is that WA will accept either a positive or a negative answer of the correct magnitude.
And did you get the news - no penalty for incorrect guesses?
In example 15.6, corners, angles, etc. make no difference. Gauss's law says the flux is proportional to the charge enclosed, which is zero. The problem with this blog is that it's not really possible to draw pictures. But notice that for each little area on the spherical surface on the x>0 side where the flux is posiive (outside of the sphere), there is an equal and opposite contribution from the x<0 side. So they cancel, and the total flux is zero.
On #12 I'm very confused! If I'm not mistaken, E = sigma / Eo...(electric field = sigma divided by 8.85e-12). The thing is, in the question a numerical value is tied in with sigma. And where do the distance values fit in? Please clarify...this problem has me stumped.
Think of sigma as being some specified charge density, whose numerical value you don't know, but you don't need. Think of one plate alone, say at z=0, first. If it had a charge density of, say, +5*sigma, the field above (z>0) the plate would be +2.5*sigma/epsilon0 (in the z direction), and for z<0, -2.5*sigma/epslion0. Note that WA wants you to fill in the numerical multiple of sigma/epsilon0, so if that were the problem, you would put 2.5 or -2.5 in the box.
Now you have to superpose two planes of charge, like I did on the last slide of Sept. 2. The big difference being that in this problem, the two planes do not have the same numerical value.
Does that clarify?
I still don't understand (I'm looking at the last slides from 9/2). Maybe I'm just missing it completely...but here's my reasoning:
E = Q / (Eo X 4pir^2)
Then, I cancelled Q/4pir^2 because that's charge per unit area, which is given in two places in the problem (the negative sigma and the positive sigma).
However, when I plug this in I get extreme numbers...nothing like the integers you just mentioned.
I think you're mixing up pieces for several different equations. E=ke * Q / r^2 = Q / (eps0*4pi*r^2) is the field a distance r from a point charge Q, or the field a distance r from the center of a sphere carrying total charge Q. But that doesn't depend on the charge density of the sphere. Anyway, in the last problem (is that what you're asking about?), we have an infinite sheet of charge, which has charge density sigma (Coul/m^2). The field from such a sheet of charge is sigma / (2*eps0), independent of the distance from the sheet.
Does that help clarify?
Can someone explain multiple choice question 11 on page 524? I don't understand how the electrons on the ground's surface and the surface of your feet repel each other as the reason why the earth isn't capable of pulling you through the ground to the center of the earth.
Thanks!
Vito, I would say that there are a few steps missing in that answer (from SV8). Matter is made of atoms, which consist of electrons which exist in a cloud around positively charged nuclei (consisting of protons and neutrons), and for the most part these are electrically neutral - same number of electrons and protons. We'll look at this much more closely at the end of the course, but I hope it's familiar from chemistry you've taken. Atoms have a size, typically 1 or 2 x 10^-10 m. If you try to push two atoms too close together, the electrons that are out at the frontier of the atoms would begin to overlap and repel each other. We know that atoms that are not too close can form chemical bonds which attract them to one another, so that whole story is rather complicated. But that is the sense in which the repulsion between two objects in contact is due to the repulsion between electrons.
I'm still not getting number 12 on WA chapter 15. The worked out example in the book is not helping. I don't understand the reason for halving the charge (i.e. from 5 to 2.5 etc.) Help!
P.S. I have not received a single correct answer regarding number 12. It either tells me I have inputted the wrong sign, or that my answer is off by more then 100%. Help!
Problem #12 is the next post planned for the video solutions.
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