How to Rank Charge Density of Conductive Spheres?

[isukatphysics69]

Homework Statement

Sphere 1 has net positive charge Sphere 2 has net negative charge Sphere 3 has net positive charge

The ranking of net charge magnitudes are
SPHERE 3 > SPHERE 2 > SPHERE 1

All spheres are conductors


Sphere 2 is moved away from Sphere 1 and toward Sphere 3 so that 2 and 3 touch.

Rank the charge density at each labeled point A -- E, greatest first. (Note that point E indicates the left side of Sphere 3; there is no labeled point on the right side of Sphere 3.)

Rank positive charge greater than negative charge. Include zero in your ranking.
HINT: Image what would happen is Sphere 1 were removed; then, consider what effect Sphere 1 has on Spheres 2 and 3 when it is present.

Homework Equations

None

The Attempt at a Solution

Sphere 3 has net positive charge and has the highest magnitude of net charge, sphere 3 is pushing the positives in sphere 2 to point C and since sphere 3 has the most net charge points E and D now have net positive charge, sphere 1 is net positive so it is pushing the positives in sphere 2 towards sphere 3 so I think C, D & E are all positively charged now and all the negative charged has transferred to the right corner of sphere 3. since sphere 1 is net positive I feel A and B are also positively charged

 

[SammyS]

Homework Statement

Sphere 1 has net positive charge Sphere 2 has net negative charge Sphere 3 has net positive charge

The ranking of net charge magnitudes are
SPHERE 3 > SPHERE 2 > SPHERE 1

All spheres are conductorsSphere 2 is moved away from Sphere 1 and toward Sphere 3 so that 2 and 3 touch.
View attachment 230361Rank the charge density at each labeled point A -- E, greatest first. (Note that point E indicates the left side of Sphere 3; there is no labeled point on the right side of Sphere 3.)

Rank positive charge greater than negative charge. Include zero in your ranking.
HINT: Image what would happen is Sphere 1 were removed; then, consider what effect Sphere 1 has on Spheres 2 and 3 when it is present.

Homework Equations

None

The Attempt at a Solution

Sphere 3 has net positive charge and has the highest magnitude of net charge, sphere 3 is pushing the positives in sphere 2 to point C and since sphere 3 has the most net charge points E and D now have net positive charge, sphere 1 is net positive so it is pushing the positives in sphere 2 towards sphere 3 so I think C, D & E are all positively charged now and all the negative charged has transferred to the right corner of sphere 3. since sphere 1 is net positive I feel A and B are also positively charged

What were the initial positions of the spheres?

 

[isukatphysics69]

What were the initial positions of the spheres?

initially 2 was in the middle, 1 was far left 3 was far right,
then
2 was touching 1 and was moved away towards 3

 

[isukatphysics69]

Need halp

 

[SammyS]

initially 2 was in the middle, 1 was far left 3 was far right,
then
2 was touching 1 and was moved away towards 3

Seems like this is the tail end of a post which has been either removed from view or deleted.

If that's so, can you at least summarize the results of those parts?

 

[isukatphysics69]

Seems like this is the tail end of a post which has been either removed from view or deleted.

If that's so, can you at least summarize the results of those parts?

Yes, I will be back momentarily with the results

 

[isukatphysics69]

Seems like this is the tail end of a post which has been either removed from view or deleted.

If that's so, can you at least summarize the results of those parts?

Three conducting spheres -- 1, 2, and 3 -- are shown below. Spheres 1 and 2 are initially neutral and Sphere 3 initially has a net positive charge. Spheres 2 and 3 are the same size, but Sphere 1 is larger, as indicated in the diagram. Note also that the center of Sphere 1 is about 10 times farther from the center of Sphere 3 as the radius of Sphere 3.

Rank the charge density at each labeled point A -- E, greatest first. Input your answer in the format A>B=0>C>D=E.

Rank positive charge greater than negative charge. Include zero in your ranking.

CORRECT ANSWER : E>C>A>0>B>DSphere 2 is moved toward Sphere 1 so that they touch.

Rank the magnitude of the net charge on each of the three spheres 1 -- 3 in the previous image, greatest first. Here, magnitude means absolute value, so ignore the sign of the charge.

CORRECT ANSWER: 3>2=1

Rank the charge density at each labeled point A -- E, greatest first. Input your answer in the format A>B=0>C>D=E.

Rank positive charge greater than negative charge. Include zero in your ranking.

CORRECT ANSWER: E>A>B=C=0>DSphere 2 is moved away from Sphere 1 and toward Sphere 3 so that 2 and 3 touch.

Rank the magnitude of the net charge on each of the three spheres 1 -- 3, greatest first. Here, magnitude means absolute value, so ignore the sign of the charge.

CORRECT ANSWER: 3>2>1Rank the charge density at each labeled point A -- E, greatest first. (Note that point E indicates the left side of Sphere 3; there is no labeled point on the right side of Sphere 3.)

Rank positive charge greater than negative charge. Include zero in your ranking.
HINT: Image what would happen is Sphere 1 were removed; then, consider what effect Sphere 1 has on Spheres 2 and 3 when it is present.

CORRECT ANSWER: THIS IS WHERE I AM COMPLETELY STUCK

 

[SammyS]

Three conducting spheres -- 1, 2, and 3 -- are shown below. Spheres 1 and 2 are initially neutral and Sphere 3 initially has a net positive charge. Spheres 2 and 3 are the same size, but Sphere 1 is larger, as indicated in the diagram. Note also that the center of Sphere 1 is about 10 times farther from the center of Sphere 3 as the radius of Sphere 3.
...

Sphere 2 is moved away from Sphere 1 and toward Sphere 3 so that 2 and 3 touch.

Rank the magnitude of the net charge on each of the three spheres 1 -- 3, greatest first. Here, magnitude means absolute value, so ignore the sign of the charge.

CORRECT ANSWER: 3>2>1Rank the charge density at each labeled point A -- E, greatest first. (Note that point E indicates the left side of Sphere 3; there is no labeled point on the right side of Sphere 3.)

Rank positive charge greater than negative charge. Include zero in your ranking.
HINT: Image what would happen is Sphere 1 were removed; then, consider what effect Sphere 1 has on Spheres 2 and 3 when it is present.

CORRECT ANSWER: THIS IS WHERE I AM COMPLETELY STUCK

I'm surprised that the answer given for magnitude in this case is correct. I would have Sphere2 > Sphere3 > Sphere1

Use the hint(s). The first part seems straight forward.

It seems clear to me which point has the greatest (positive) charge density What do you think it may be?

 

[isukatphysics69]

I'm surprised that the answer given for magnitude in this case is correct. I would have Sphere2 > Sphere3 > Sphere1

Use the hint(s). The first part seems straight forward.

It seems clear to me which point has the greatest (positive) charge density What do you think it may be?

I think E has the greatest charge density

 

[SammyS]

I think E has the greatest charge density

Why is that?

Notice the answers for Spheres 1 and 2 touching?

 

[isukatphysics69]

Why is that?

Notice the answers for Spheres 1 and 2 touching?

I was thinking that E is the greatest because 3 has the greatest net charge and it is a positively charged sphere

 

[isukatphysics69]

My thinking was E>C>B>0>A>D

Sphere 3 has greatest net charge and positive, so it is E with the greatest, then that positive charge is pushing the positives in sphere 2 to the left so C is also positive but now as I am typing this I think B is before C

 

[SammyS]

I was thinking that E is the greatest because 3 has the greatest net charge and it is a positively charged sphere

Yes, but 2 and 5 are touhing and they're conductors. What effect does 1 have on them?

 

[isukatphysics69]

Yes, but 2 and 5 are touhing and they're conductors. What effect does 1 have on them?

1 is polorizing them pushing the positives to the right

 

[isukatphysics69]

So where do the negatives in the net negative sphere 2 go? its so confusing because you have 1 polorizing from the left and 3 polorizing on the right but 3 is more powerful so it should be pushing the positives to C but I don't know what happens to the negatives from 2, do they just go to the right corner of 3?

 

[SammyS]

1 is polarizing them pushing the positives to the right

Oh ! I mis-read the answer to the case of 1 and 2 touching.

 

[SammyS]

My thinking was E>C>B>0>A>D

Sphere 3 has greatest net charge and positive, so it is E with the greatest, then that positive charge is pushing the positives in sphere 2 to the left so C is also positive but now as I am typing this I think B is before C

I doubt that A is negative, likewise doubt that B is positive. The side of Sphere 1 closest to the Spheres 2&3 should have positive (like) charge driven to the far side and negative (unlike) charge attracted.

 

[isukatphysics69]

I doubt that A is negative, likewise doubt that B is positive. The side of Sphere 1 closest to the Spheres 2&3 should have positive (like) charge driven to the far side and negative (unlike) charge attracted.

Im wondering what happens to the negatives from the net negatively charged sphere 2?

 

[isukatphysics69]

Im getting really pissed off at physics right now

 

[SammyS]

Im wondering what happens to the negatives from the net negatively charged sphere 2?

They are neutralized by some of the positive charges which make up the net positive charge of Sphere 3. After all, they're conductor making contact..

 

[Delta2]

Since 2 and 3 touch and have exact same geometry, I expect 2 and 3 to have exact same charges (both positive if understood correctly the previous processes that lead to this setup). But after we examine the effect of sphere 1, 2 will have abit less positive charge and 3 abit more positive charge since the net electric field inside 2 and 3 must cancel the electric field from sphere 1. So indeed it will be 3>2>1 for the charge.

And for the charge densities, it will be C>A>D=E=0>B

 

[isukatphysics69]

They are neutralized by some of the positive charges which make up the net positive charge of Sphere 3. After all, they're conductor making contact..

So my understanding at this time is all of points are positive. My professor told me earlier that the combination of spheres 2 and 3 are not polorizing sphere 1 enough to make point B negative, I was just confused about the contact between them because I don't know how much more sphere 3 is positive than sphere 2 is negative and I didn't know if it was only slightly more it would be able to neutralize

 

[isukatphysics69]

Since 2 and 3 touch and have exact same geometry, I expect 2 and 3 to have exact same charges (both positive if understood correctly the previous processes that lead to this setup). But after we examine the effect of sphere 1, 2 will have abit less positive charge and 3 abit more positive charge since the net electric field inside 2 and 3 must cancel the electric field from sphere 1. So indeed it will be 3>2>1 for the charge.

And for the charge densities, it will be C>A>D=E=0>B

Hey man thank you for your time but please do not tell the answers, that is incorrect but in the future please do not just tell the answer thank you

 

[Delta2]

Ok I am sorry, can you tell me the web page to check myself, I did the mistake of taking B as negative but now I realized this is not the case. (and also D=E=0 doesn't look quite correct ).

 

[isukatphysics69]

Ok I am sorry, can you tell me the web page to check myself, I did the mistake of taking B as negative but now I realized this is not the case. (and also D=E=0 doesn't look quite correct ).

I am logged into my personal moodle account so I cannot share the web page unfortunately

 

[isukatphysics69]

right now I was thinking E>D>C>A>B>0 but that was also incorrect

 

[Delta2]

I was thinking C>A>B>E=D=0 but hard to explain my reasoning.

I ask for this : What is the net charge of sphere 2 on her way to touch the sphere 3 and before the touch. If I understood correctly sphere 2 has negative charge and in absolute value smaller than the positive charge of sphere 3. Is that correct?

 

[SammyS]

Look at part 1 of the hint again.

 

[isukatphysics69]

I was thinking C>A>B>E=D=0 but hard to explain my reasoning.

I ask for this : What is the net charge of sphere 2 on her way to touch the sphere 3 and before the touch. If I understood correctly sphere 2 has negative charge and in absolute value smaller than the positive charge of sphere 3. Is that correct?

Incorrect@SammyS I think I know what you are saying, so I am only looking at half of the charge in sphere 3 so E = C = D?

Nvm that is wrong toohow does C > D = E sound

 

[isukatphysics69]

I was thinking C>A>B>E=D=0 but hard to explain my reasoning.

I ask for this : What is the net charge of sphere 2 on her way to touch the sphere 3 and before the touch. If I understood correctly sphere 2 has negative charge and in absolute value smaller than the positive charge of sphere 3. Is that correct?

Also yes you are correct with reasoning but not answer

 

[Delta2]

Also yes you are correct with reasoning but not answer

You mean I am correct as to my comment on the net charge of sphere 2 before it touches sphere 3?

Anyway I haven't run into many problems of this type so I ll stop of making guesses . I think this problem is made to check the understanding of the electrostatic induction and the equipotential process when the spheres touch.

 

[isukatphysics69]

You mean I am correct as to my comment on the net charge of sphere 2 before it touches sphere 3?

Anyway I haven't run into many problems of this type so I ll stop of making guesses . I think this problem is made to check the understanding of the electrostatic induction and the equipotential process when the spheres touch.

yes that's what I meant an yea that's what this problem is I will drop out and work on cargo ship this is too complicated

 

[SammyS]

Incorrect@SammyS I think I know what you are saying, so I am only looking at half of the charge in sphere 3 so E = C = D?

Nvm that is wrong toohow does C > D = E sound

 

[SammyS]

C > D = E makes sense if we remove Sphere 1. The majority of excess charge mill migrate to the far ends the 2,3 combination, that is C and the unmarked right side of 3. Density at D,E will be much less.

Then, bring Sphere 1 back. Remember, its still relatively far away and has the smallest net charge.

I suspect the right hand side of 3 has largest density, then C > A ?? E > D ?? >0 not sure where B goes.

Maybe between A & E, else between D and 0 .

 

[isukatphysics69]

C > D = E makes sense if we remove Sphere 1. The majority of excess charge mill migrate to the far ends the 2,3 combination, that is C and the unmarked right side of 3. Density at D,E will be much less.

Then, bring Sphere 1 back. Remember, its still relatively far away and has the smallest net charge.

I suspect the right hand side of 3 has largest density, then C > A ?? E > D ?? >0 not sure where B goes.

Maybe between A & E, else between D and 0 .

Thank you for reply, I will read tomorrow and give this another shot. 8 hours spent on this today and got nowhere I think I am done for today

 

[Delta2]

C > D = E makes sense if we remove Sphere 1. The majority of excess charge mill migrate to the far ends the 2,3 combination, that is C and the unmarked right side of 3. Density at D,E will be much less.

Then, bring Sphere 1 back. Remember, its still relatively far away and has the smallest net charge.

I suspect the right hand side of 3 has largest density, then C > A ?? E > D ?? >0 not sure where B goes.

Maybe between A & E, else between D and 0 .

I perfectly agree to what you say here.

Also I think it should be C>A>B>E>D>0, I expect E and D to be very close to zero but it might be E>D>0 due to the field effect from the sphere 1. B has to be very close to A cause the field inside the sphere 1 must be zero (B will be slightly smaller due to the fact that it is closer to the other two spheres that have net positive charge as a whole).

 

[SammyS]

A general question of clarification for @isukatphysics69 .

Referring to specific details concerning the physical situation depicted in the figures.

Initial figure for example:

Do the labels:

1) refer to individual points on the surfaces of the spheres located on the line joining the centers of the spheres?
2) refer to individual points on the surfaces of the spheres located close to the line joining the centers of the spheres (or to a small region at such a location)?​

.
I suppose I have been thinking of the labeled points in the 2nd way (small regions), but as I reconsider this, it now makes more sense to suppose that the 1st way is what was intended for this question. If this is the case, then go back to the charge density answer for the case where Spheres 1&2 touch:

which was given as: E>A>B=C=0>D .
(Charge density at) both B and C should be zero. (What the feather! That's what it did say all along !) I mis-read this too ! DUH on me !
Well this must be the case at this position with the two conductors touching along the line connecting the centers.

So...
The same must be true in the final case, where Spheres 2&3 touch, only this time D and E touch, so charge density there is zero.

My apologies to @isukatphysics69

 

[isukatphysics69]

A general question of clarification for @isukatphysics69 .

Referring to specific details concerning the physical situation depicted in the figures.

Initial figure for example:

View attachment 230401

Do the labels:

1) refer to individual points on the surfaces of the spheres located on the line joining the centers of the spheres?
2) refer to individual points on the surfaces of the spheres located close to the line joining the centers of the spheres (or to a small region at such a location)?​

.
I suppose I have been thinking of the labeled points in the 2nd way (small regions), but as I reconsider this, it now makes more sense to suppose that the 1st way is what was intended for this question. If this is the case, then go back to the charge density answer for the case where Spheres 1&2 touch:
View attachment 230402
which was given as: E>A>B=C=0>D .
(Charge density at) both B and C should be zero. (What the feather! That's what it did say all along !) I mis-read this too ! DUH on me !
Well this must be the case at this position with the two conductors touching along the line connecting the centers.

So...
The same must be true in the final case, where Spheres 2&3 touch, only this time D and E touch, so charge density there is zero.

My apologies to @isukatphysics69

I am back and I have tried a few attempts before coming back to the forum and nothing yet. @Delta² that was an incorrect answer. @SammyS my professor said to look at regions D and E as regions in this problem and not points, so I do not believe that I am supposed to have D=E=0 here but I could be wrong

 

[isukatphysics69]

I tried C>A>E>D>B>0 and was really confident about that one but incorrect

 

[SammyS]

I am back and I have tried a few attempts before coming back to the forum and nothing yet. @Delta² that was an incorrect answer. @SammyS my professor said to look at regions D and E as regions in this problem and not points, so I do not believe that I am supposed to have D=E=0 here but I could be wrong

Well, is the same true for B and C: regions rather than points.
If so, I don't see how they can be zero in the previous situation. Just saying.

I tried C>A>E>D>B>0 and was really confident about that one but incorrect

I still think E and D must be very small, and I don't think that B is very much less than A. It is stated that there is relatively large separation.

I don't know if you have tried this yet:

C > A > B > E > D > 0

My best guess.

 

[isukatphysics69]

Well, is the same true for B and C: regions rather than points.
If so, I don't see how they can be zero in the previous situation. Just saying.I still think E and D must be very small, and I don't think that B is very much less than A. It is stated that there is relatively large separation.

I don't know if you have tried this yet:

C > A > B > E > D > 0

My best guess.

That was actually the most recent one that I tried and it was incorrect, and there was a reason I believe that the previous one was 0, I think it had something to do with both spheres having equal net charge, now both spheres in contact do not have equal net charge

 

[SammyS]

That was actually the most recent one that I tried and it was incorrect, and there was a reason I believe that the previous one was 0, I think it had something to do with both spheres having equal net charge, now both spheres in contact do not have equal net charge

The spheres did have equal net charge in the previous case, but Sphere 1 is larger, so it has greater surface area, so I would expect the surface density would less at C than at B (because of signs), but less in magnitude at B than at C, although, I would expect both to be very small in magnitude.

We can speculate some more. Right now I'm out of guesses.

Got any ideas you want to run up the flag pole?

EDIT ed above as shown in red

 

[isukatphysics69]

The spheres did have equal net charge in the previous case, but Sphere 1 is larger, so it has greater surface area, so I would expect the surface density would less at C than at B (because of signs), but less in magnitude at B than at C, although, I would expect both to be very small in magnitude.

We can speculate some more. Right now I'm out of guesses.

Got any ideas you want to run up the flag pole?

EDIT ed above as shown in red

I am absolutely stumped, so sphere 3 has the most net charge, as sphere 2 is moving toward sphere 3, id imagine that at around the three quarters mark nearest sphere 1, the power of sphere 3's polarization will take over and start really pushing the positives to point C and negatives to point D, so now when they come in contact the negatives are at D and positives are at point C and then they will neutralize. after neutralization the net positive will push more positives to A and B will still be positive but not as positive as A

 

[isukatphysics69]

I am just absolutely stumped I've never spent 10 hours on a single problem before this is crazy

 

[Delta2]

I am intrigued to see what's the correct answer here, don't forget to write the answer here please, after your teacher tells it to you.

 

[isukatphysics69]

I am intrigued to see what's the correct answer here, don't forget to write the answer here please, after your teacher tells it to you.

I will, I don't think he will tell me the right answer until the submission option is closed tho which won't be until September 14th. I will continue trying until then

 

[isukatphysics69]

Also guys before I go to sleep I will leave the messages that my professor has sent to me to try to help without giving away too much, maybe there is a clue I am missing here...

First:

I stepped out for a couple minutes around that time, I'm back now. For 5, there is a transfer of charge between spheres 2 and 3 when they are in contact. The net charge on both spheres would be 0 if both spheres had the same amount of charge, with one + and the other - (and if 1 were not present). However, the charges are not equal. 2 got its charge from 1 through polarization while they were in contact. 1 and 2 were pretty far away (compared with the radius the spheres) at that time, so there was only a small amount of charge separation, much smaller than the net + charge on 3.
Second:

The questions all occur in sequence, unless it specifically says otherwise. Sphere 2 was moved to contact sphere 1 for questions 2 and 3. That made sphere 1 have net + charge and sphere 2 net -charge. Now, for questions 4 and 5, sphere 2 is moved from contact with sphere 1 and made to touch sphere 3. Here D and E don't represent the same point. D is the right side of sphere 2 and E is the left side of sphere 3, not just the one point of contact. Also, note that the + charge in spheres 2 and 3 will not be concentrated in the middle. The + charges there repel each other and want be as far away for each other as possible, which would put them mostly on the outside parts of the spheres with less in the middle.
Third:

Consider what happens bit by bit and then put it together. When 1 and 2 were touching, 1 had net + and 2 had net -. After separating them, this is still true. When 2 touches 3, charge will transfer. 3 had more + than 2 has -, so the combination is net +. If 1 were absent, this charge would be shared equally between 2 and 3, with more charge on the outside (left side of 2 and right side of 3) and less in the middle. With 1 present, the + in 1 will push some + from 2 to 3, but not a lot (+ in 1 would be much less than originally in 3 and it's pretty far away compared to the size of 3). The same thing happens in 1. 2 and 3 are both +, so that will push some + in 1 from B to A, but not a lot (not so much that B is made -). I hope that helps. Let me know if you have more questions.

 

[isukatphysics69]

@SammyS @Delta² Messages from professor above

 

[Delta2]

Yes all these points are kind of known to me and they were lead me to think that C>A>B>E>D>0. Hmm your teacher says that the charge in sphere 1 is much smaller than that of sphere 3, maybe try C>E>D>A>B>0 as last try for me, though I still don't think that's the case. For me C>A>B>E>D>0 is the correct one.

 

[SammyS]

I am absolutely stumped, so sphere 3 has the most net charge, as sphere 2 is moving toward sphere 3, id imagine that at around the three quarters mark nearest sphere 1, the power of sphere 3's polarization will take over and start really pushing the positives to point C and negatives to point D, so now when they come in contact the negatives are at D and positives are at point C and then they will neutralize. after neutralization the net positive will push more positives to A and B will still be positive but not as positive as A

As Sphere 2 goes from touching Sphere 1 and then moving towards Sphere 3, Sphere 2 has much less net charge than Sphere 3. That's because the fact that Spheres 1 & 2 have any net charge is due to the polarization produced by the Electric field due to Sphere 3.

By the way: Did I see somewhere (maybe in your old thread) some statement about the distances relative to sphere size?​

You're right, as Sphere 2 approaches Sphere 3, a lot of polarization occurs on Sphere 2.but not much on Sphere 3, because of the very different amount net charge on these two spheres.

As for Sphere 1, when it and Sphere 2 just separate, points B and C have charge near zero, similar to when they were touching. As Sphere 2 moves away point B gains a little positive charge and point A looses some. Don't forget. These are conductors. The (like) charges on the surface are also repelling each other.
...

Just now I see the responses from your prof.. I generally agree with them.

@Delta² 's idea in Post #49 looks reasonable..