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Correct answer but completely wrong coneptual argument and Physics master didn't object!!

Main post link -> https://brilliant.org/assessment/s/mechanics/4583580/

In this particular problem (which I also solved), a solution which has been submitted is completely wrong conceptually. Solution says that centrifugal force is balanced by Lorentz force. Of course in our frame there would be no centrifugal force since our frame is inertial. I objected to that argument by adding comment below the solution itself. I thought that at least person who presented argument would reply or at least Physics master would reply. But nobody is replying there which is surprising for me. People who did not solve this and read this solution may get wrong physical picture and for these people it is important to clarify logical fallacy of the argument. Would Physics master please take note of it??

Note by Snehal Shekatkar
3 years, 11 months ago

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A comment has been made in this solution discussion. Note that I really try not to comment on solutions too much as I'd far rather you comment on each other solutions. I do not want our discussions to become too much like "school", where you submit solutions and I mark them right/wrong. Brilliant is about community, and discussions should be primarily among peers where I only chime in occasionally to give an extension of the problem or something.

However, Snehal is correct that in this case the conceptual issues were not addressed by the community for quite a while and that this solution discussion needed some love. Thanks for bringing it to our attention.

David Mattingly Staff - 3 years, 11 months ago

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I don't understand how people talk about wrong things and get away. For another example, please look at the solution of this problem about aurora also posted last week itself. Even in this solution it has been said that centrifugal force is balanced by Lorentz force!! I agree with you David sir that Brilliant should not become like school. But if you don't comment anything about obviously wrong things, then people who study solutions would learn wrong things. I personally think that this is very bad and it is our duty to prevent this. I would like to know your view. Thank you.

Snehal Shekatkar - 3 years, 11 months ago

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My view is the following. I would hope that the members of the Brilliant community, rather than asking the Challenge masters to step in on a point, would simply make that point themselves in the discussion. The discussion below between you and Josh S. illuminates exactly what we want to see on Brilliant. You are discussing a physical issue, you are both presenting your arguments, you're being reasonably civil (although watch words like "pathetic" :) ), and the conversation is illuminating to everyone who reads it.

The goal in giving out weekly problem sets and opening solution discussions is to provide topics for you all to discuss and debate, not me. Hence you will find me very reticent to step in unless an incorrect solution is languishing for a long period of time. If you feel like solutions are wrong or that physics issues are unclear, simply bring it up in a respectful and thorough manner right in the discussion. If you're right in general, you'll become known on Brilliant, be respected by the community, and make the community and world a little bit better of a place.

David Mattingly Staff - 3 years, 11 months ago

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I agree with the spirit of a campaign like this (to demand correct solutions) but in this case I don't see the point. Yes, a centrifugal force is an artifact of rotating reference frames, but guess what! If we move to a rotating reference frame, the "centrifugal force" is just as useful as if we'd insisted on the more puritanical program of identifying the central force as giving rise to a circular motion. No wonder then that in performing calculations for a physics and math puzzle site, one might resort to calculating devices that end in the same place as the orthodox analysis! Xkcd has made the point:

Xkcd

Xkcd

And here is Lubos making the same point: Lubos Motl discussing rotating reference frames

I would kindly ask you to identify a situation whereupon making a transformation into a rotating reference frame, and inserting the required fictitious forces, one goes awry in their analysis? Reference frames, inertial and non-inertial are used all over physics to calculate and there's no harm in using them.

Josh Silverman Staff - 3 years, 11 months ago

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@Josh Silverman Its pathetic that you are showing a cartoon to me and trying to make me understand that centrifugal force is real in noninertal frames. I know that very well man! In the solution, did you ever say that you are doing calculations in noninertial frame? And yes.. if you were really doing calculations in rotating frame, charge should have been stationary in that frame but you are saying that velocity vector is pointing in this and that direction and so on. Now you decide which frame you are working in and if you have made mistake then better accept it instead of trying to defend it. Thank you

Snehal Shekatkar - 3 years, 11 months ago

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@Snehal Shekatkar Well... alrighty then. I'm not looking to cast aspersions on one another.

In the solution, did you ever say that you are doing calculations in noninertial frame?

On the specific point, I didn't say "this calculation is being performed in a rotating reference frame", as you wish I would have done. On the other hand, I was using the concept of a centrifugal force which is, explicitly, a tool that's used to solve problems inside of rotating reference frames, so I don't see why you are so convinced I was unaware I was calculating in the rotating frame. It's okay if you don't believe me, I don't care that much.

And yes.. if you were really doing calculations in rotating frame, charge should have been stationary in that frame

Yes, in a rotating reference frame, the charge is not rotating. Just as in a rotating reference frame, a car that's going around a bend or a seat on a carousel are also not rotating, yet the passenger will feel the wall pushing against them in both of those cases. You maintain the force from the inertial frame and balance it with a fictitious centrifugal force which is just the same as identifying the real force as a central force. That is how such a calculation is carried out. I don't understand why you think I'm trying to pull one over on you. If there is some other problem you can find with the argument, please bring that to light, but if you're on about me knowing about my choice of a rotating reference frame I don't know what to tell you.

And again:

I would kindly ask you to identify a situation whereupon making a transformation into a rotating reference frame, and inserting the required fictitious forces, one goes awry in their analysis? Reference frames, inertial and non-inertial are used all over physics to calculate and there's no harm in using them.

Josh Silverman Staff - 3 years, 11 months ago

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@Josh Silverman Lets talk about physics. For a moment let us assume that you were doing calculations in rotating frame only (the frame attached to the particle). In this frame there will be a centrifugal force. But there will be no \(q(v\times B)\) force since \(v=0\). Thus you cannot 'balance' centrifugal force and '\(q(v\times B)\)' forces because one of them does not exist!! Actually the magnetic part of Lorentz force does not exist at all in that frame. In rotating frame, force acting on the particle will be electrical and that will not be 'balanced' by centrifugal force. Rather, that electrical force will 'act as' a centrifugal force.

Also, I never wanted to say anything personally to you. Please forgive me if at any point I was rude. I think we are all nice people and would like to maintain that. :)

Snehal Shekatkar - 3 years, 11 months ago

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@Snehal Shekatkar

Also, I never wanted to say anything personally to you. Please forgive me if at any point I was rude. I think we are all nice people and would like to maintain that. :)

Cool, I agree!

Lets talk about physics.

Yes.

Rather, that electrical force will 'act as' a centrifugal force.

Would you argue that the magnitude of this force is different from or the same as the magnitude of \(q\left(\vec{v}\times \vec{B}\right)\) in the stationary frame?

Josh Silverman Staff - 3 years, 11 months ago

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@Josh Silverman No. The magnitude of the electrical force acting on the charge in rotating force will be exactly equal to magnitude of magnetic force acting on it in our frame and that is the very reason that your answer is right. Now see all my comments.. I never said that your answer is wrong. What I am saying is that the conceptual arguments that you are presenting are wrong. See.. may be all these subtleties you already are aware of.. but of course that is not the point because then you are not trying to learn anything new from your own solution. Think of a person who could not solve this particular problem and ended up reading your solution to learn physics involved in the problem. Now he will learn following things from this solution: 1)In our frame centrifugal force exists (Because you didn't mention that you are working in rotating frame). 2)If someone realizes that you are indeed working in the rotating frame, then he will think that in that frame magnetic force exists whereas it doesn't, only electrical force exists. 3)He will also think that apart from magnetic force, another force called 'centrifugal force' exists and these two forces are 'balanced'. Of course nothing is balanced really.. that electrical force acts as a centrifugal force in reality.

Now tell me my dear friend , if conveying all such things is good or bad to a person who is trying to learn physics involved using your solution. In my view, it is not. I think I will stop here. Thank you :)

Snehal Shekatkar - 3 years, 11 months ago

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@Snehal Shekatkar

No. The magnitude of the electrical force acting on the charge in rotating force will be exactly equal to magnitude of magnetic force acting on it in our frame and that is the very reason that your answer is right.

OK, we agree on this.

Now see all my comments.. I never said that your answer is wrong. What I am saying is that the conceptual arguments that you are presenting are wrong.

If we get a right answer by making some wrong argument, I would want to fix the argument.

See.. may be all these subtleties you already are aware of.. but of course that is not the point because then you are not trying to learn anything new from your own solution. Think of a person who could not solve this particular problem and ended up reading your solution to learn physics involved in the problem.

I think I understand the point. I am not sure I have a philosophy about the solutions that I write here but I think what I try to do is to replicate my thought process as close as I can and to add some justification along the way in places I may have skipped ahead by intuition or past experiences (and of course waste at least 20 minutes drawing diagrams).

I do learn new concepts or see new insights on Brilliant by reading the other solutions and I enjoy that. I would certainly be happy if people could have a similar kind of a learning experience from my solutions that I sometimes have on others.

But... I don't think of Brilliant as a learning site for physics. Some of the problems here assume a decently high level of previous physics knowledge and the learning that I get out of Brilliant is more along the lines of seeing the insight of the other problem solvers and the connections that they're able to make, not to learn about fundamental concepts.

I would hope that somebody who couldn't solve the problem would read the posted solutions and try to independently verify them. Sometimes this might involve reading and research into the techniques being used.

When I use methods that I think are far afield from the typical approach, like when I used the calculus of variations to solve the GRIN light guide problem, I usually devote more attention to bringing the technique or subject up to speed, justifying every little detail, and providing links to external resources to learn about them. I don't think this problem required that level of treatment.

Also, I am not sure that I agree with making every last justification in the first place. For instance, I prefer to have a hint or a guide to a solution rather than the explicit solution itself. A lot of my learning takes place by struggle and repeated failure. Maybe I have hit the wrong balance of information and explication on this solution. I never learned much by reading extremely detailed solutions, I always benefit from the pain of wondering and struggling about certain missing details.

Also, I don't actually go through the thought process in this much detail when I write solutions so this is all hindsight and rationalization.

Now he will learn following things from this solution: 1)In our frame centrifugal force exists (Because you didn't mention that you are working in rotating frame).

I don't agree with this. I think if somebody read my solution and didn't understand what a centrifugal force is, the first thing they should do is to look it up and at least read its definition. If they did that, they would immediately learn that centrifugal force only exists in rotating frames. If they didn't at least look that up I would have a hard time believing they were actually trying to understand the solution. Of course, if they already understand what a centrifugal force is they should be clear that I'm working in the rotating frame.

2)If someone realizes that you are indeed working in the rotating frame, then he will think that in that frame magnetic force exists whereas it doesn't, only electrical force exists.

I agree this could be confusing. But also, it is true in general that changing into a rotating frame can't change the physics (the actual outcome, independent of the calculation method). This may be one of the points where I erred on the side of too little explaining. I don't disagree.

>3)He will also think that apart from magnetic force, another force called 'centrifugal force' exists and these two forces are 'balanced'. Of course nothing is balanced really.. that electrical force acts as a centrifugal force in reality.

Would the electrical force really act as a centrifugal force? The centrifugal force points from the center of the path towards the particle. But on the larger point of this being a potential source of confusion, I don't disagree with what you're saying on principle.

Now tell me my dear friend , if conveying all such things is good or bad to a person who is trying to learn physics involved using your solution. In my view, it is not.

Maybe, maybe not. Even if I presented every last detail of my arguments there will still be people who don't find it useful for other reasons, perhaps because they dislike the idea of using a rotating frame in this situation.

For example, I really like Mark and Đinh's solutions, but I am not sure I would have ever thought to do the problem in the way that they did and I am not sure how much my learning of their thought process on the problem will influence my problem solving approach in the future. At other times, each of them have posted solutions that did affect my thought process on a later problem, for better or worse.

I don't see Brilliant as a place for learning textbook physics and detailed explanations. I don't think it's realistic to achieve that simply by reading solutions. It requires a lot of self study and reading and thinking to get that kind of an experience.

In any event, even if I don't want to deep down, I am sure the experience of this discussion will make me think twice about the level of explanation I give to different points. Maybe you will like them more in the future!

I think I will stop here. Thank you :)

I think I understand your point now. I will still use centrifugal forces when I can but I will always see your face when I do. I will also stop to think about how I may be confusing some people.

Josh Silverman Staff - 3 years, 11 months ago

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Also I request you David sir to write solution for this aurora problem also just as you did for other problem.

Snehal Shekatkar - 3 years, 11 months ago

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Also note that the link you provided isn't accessible to other users. Here's the link you should give if you want to share the problem with other users. :)

Sreejato Bhattacharya - 3 years, 11 months ago

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Oh, sorry for the mistake. I am correcting it in the solution discussion. I accidentally unsubscribed myself from the discussions feed, which is why I didn't reply.

Sreejato Bhattacharya - 3 years, 11 months ago

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Oh.. I see.. Thank you.. :)

Snehal Shekatkar - 3 years, 11 months ago

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Yes.. there is no centrifugal force.. Hopefully staff would note it..

Shubhangi Atre - 3 years, 11 months ago

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