When a cylindrical capacitor formed by two concentric shells (inner shell at potential V, outer shell grounded) is connected through a resistance R, the charge decays over time following the equation Q = Q₀e^(-t/RC), where Q₀ = 2πVHε₀ln(B/A). Due to electromagnetic induction, a changing electric field induces a magnetic field, which in turn induces an EMF that opposes the original charge change, introducing an additional component C' = N₀μ₀N₀ in the circuit equation.
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Flying with Physics part 5
Added:Hey, good morning everyone. So, this is my fifth video in Flying with Physics.
Uh I would like to bring in a different thing today before we go into a one interesting problem and discussion. So, I'm arranging a kind of free mock test at the level of 10 plus two physics olympiad on 23rd August 2026 from 9:00 to 10:30 a.m.
So, and this is also followed a demo.
So, during that time only there will be a mock test and a demo class. This mock test you can use any book, any I chat GPT, whatever you like uh to take your help. So, this is really primarily online uh and for that online mock test you have to register through a WhatsApp number. Let me show you this WhatsApp number.
So, you can note this down. So, you have to register through this WhatsApp number. This is 8617215384.
So, you once you register this through this WhatsApp number, uh what I will do, I will going to send you the question paper basically for that particular mock test on that day at 9:00 a.m.
And you have to submit your answers uh you have to do it in your I mean plain paper.
And after you complete that question answers in your plain paper, this is not a kind of all multiple choice. This I would I mean this is basically you have to answer the script because the pattern, the way you are going to solve the problem does make sense difference.
So, that's important and that's why you have to do that solutioning over there in the paper itself and then once you have done that solutioning in the paper, you have to kind of send that to take a photo of your answer sheets, your name, okay, and your school uh and your phone number basically. You have to put those details. There will be a kind of you can write it down in your paper in plain and then just take a photo of that and send it to this return it back into this same WhatsApp number.
What I'm going to do, I'll evaluate for whoever is actually doing going ahead with this mock test.
Uh this evaluation will take a bit of time. So, I'll get back with the result by 6th of September, around 6th of September, I'll be providing a result.
So, so that that result is you can see.
Okay?
And um this is the So, this is what I'm focusing for and there is a reason behind doing this. Just note this number again. I'll repeat it. 8617215384 through which you have to register.
Uh there are many reasons for having this mock test. I don't know how many of you have actually seen the result of the physics olympiad, the international physics olympiad, which was held in Colombia this year. India performed very well there. Okay?
So, we have to kind of I mean, bring keep that legacy and we have to improve on that.
So, that is one of the objective. I would like to kind of make this awareness across the different sections of the student who are particularly interested in becoming I mean, doing something ground-breaking on science, physics. Okay? And of course, these are the platform through which you can get there.
And these are of course, for the competitive exam also, whoever is actually appearing for IIT JEE or in any ET, for them also, this is helpful, very much helpful.
So, um So, this is the objective as I said. So, again, I'll repeat once again. So, I'm organizing a free mock test at level of 10 plus 2 for physics olympiad on 23rd August 2026 from 9:00 to 10:30 a.m.
Along with that mock mock test, there is a demo at that particular time. Just a free demo again. This mock test, you can use any book, AI, ChatGPT, whatever you like, okay, to solve your problem.
Uh but be careful. Um, do not rely on AI and ChatGPT blindly because my I have done everything. I have tried all those things. I have already kind of They will not give you always the appropriate or correct answer. So, you have to kind of bring your own brain here and use your own brain. That's why this is a challenge. I would request that whoever is actually uh, inte- interested in taking that challenge, please go do go ahead and do so because in any case it's a free. It doesn't going to cost you anything.
Uh, and this is happen- For that, the only thing you have to do you have to register through this WhatsApp number.
Again, I'm repeating this WhatsApp number. What's 8617215384.
That's all. Nothing else you have to do.
But be Please do the registration as early as possible, preferably before 15th of August. Okay?
So, that I can compile whoever is interested, I can share the question papers to those those persons. And not only question paper, I'll share also the demo class link so that you can join the demo class.
Question paper, as I said again, I'll repeat You have to answer in a just a plain paper, fullscape paper with your name, your school, college, and your mobile number.
Okay? And in if in in in the class you are reading in, let's say, uh, if you're in college, you have to put your year, which year you are in.
And then you send it back into the same WhatsApp number. I'll evaluate it and I'll give you a res- result like where you stand in terms of your physics Olympiad and what is your What is your um, areas you will need to improve actually.
This will just not be a marking because the marking will not give you wh- what is your uh, strength and what is your weakness. I'm going to give give that details on 6th of September. Okay?
Um, now let's go to the interesting problem that I was talking about. Okay? I'll come to this problem. This is a very interesting problem wherein what has happened This is a kind of a um, two concentric cylindrical shell.
Now, the inner shell was initially kind of put a potential of V and the outer shell is grounded.
And after it was after short while after this potential was added, the the outer shell was grounded and then suddenly that that the source original source of this potential was disconnected and the two shells the two cylindrical shells were connected through a resistance R as you can see here.
So, what will happen as you can as you know very well from your basic physics concepts, these two cylindrical shell will work as a cylindrical capacitor.
So, the charge that it get gets in due to that potential V will start discharging because of this R, the red resistance that has been added. Now, what will happen this at any point in time the charge within that cylindrical shell will decay over time and that that column I mean the decayed equation is like Q0 1 - E. This is what you get. Now, Q0 you have to prove this that this is how it will decay. Q0 will be 2 pi V H epsilon 0 log B by A. B and A are the resistance sorry radius of the different two cylindrical shells. And C' is a something as an additional component that will come in because of the electromagnetic induction. What will happen? Because your charge is decaying and that decaying charge will cause a change in electric field. And that change in electric field also kind of induce a magnetic field within that particular annular space.
And that is a free space. I have not included in dielectric here. So, when that magnetic field changes over time, it in turn will induce an electro magnetic EMF as per Faraday's law.
And that EMF will again kind of some have an impact onto the your I mean the way the overall circuit is behaving and that's why this C' component will come and this C' component looks like this one. N0 mu0 N0 is nothing but the your I mean Faraday's induction constant I would say.
Uh which is actually the electromagnetic constant uh electromagnetic uh induction constant. The way we actually have the induced EMF equal to a constant N zero into the change of change rate of change of magnetic flux. From that this N zero comes.
And the remaining of the things are you can see from the geometry itself or the figure itself. H is the height. B and A are the radiuses, one internal and one another external.
And that that's what you will get. Okay?
So as I said, C dash is the constant that appears due to the induced magnetic field which in turn induces a EMF opposing the original rate of change of the rate of change of the charge.
So this is a problem, quite interesting problem. This involves actually uh Maxwell's equation. We have to introduce a Maxwell's equation here.
Uh so it is actually kind of two equations which is guiding this primarily. One is uh your um rate of change of electric field induces a magnetic field and again that again that magnetic field is also that changing. It will not be constant.
So rate of change of that magnetic field in turn will induce a EMF. That EMF will actually try to oppose the original source which has caused it. So those kind of things will come into the picture of this solution.
I'd not say it's very I mean difficult as such but you have to apply those concepts uh clearly in order to solve this. Then you can get the solution easily.
Okay, I'll end this video for today but here.
Um please as I said again, I'll repeat, please register for this mock test. Uh this will help you to judge your capability.
Uh if you're appearing for IIT JEE or if you're appearing for NEET or if you're appearing for physics Olympiad or you in general would like to get into a ground break breaking areas of science and technology, this will give you an insight into what is your capability.
What is your strength? What is your weakness? This will not be a marking that if you give a kind of competitive exam, what will happen? You are going to be giving an MCQ. So I would actually will get whether it's plus or minus.
It's a binary answer.
You don't need to you don't come to know exactly most of the time what is your areas that you really need to improve.
So that you don't understand. Okay, you might be having a lot of internal exams where you might be getting but even then that doesn't go into that detail. So when I'm going to give you a result of this particular question paper or answers, I'm going to give you that. So I'm going to clearly tell you what is your strength, where you have done good and where where you have to actually work upon in terms of your concept, in terms of your understanding. Okay, that will definitely help you in any exams that you are going to give particularly at this level.
So I would request again to please do register for this. And to to register for this, use this WhatsApp number 8617215384.
Just send your name, your school or college and your mobile number. My number in any case I'll get because if when you are doing but even then then if it is if it is not correct, you send me the WhatsApp mobile number.
I'll register you for this exam and I'll share share you the questions paper accordingly whoever get is registered and also that demo class link.
Online demo class link.
So thank you again.
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