Some formulas (electromagnetism)

[DesertFox]

dH=dl/dt
dB=dl/dx
dE/dB=-dx/dt
dD=dl/dx
dH/dD=-dx/dt

H - magnetic field strength;
B - magnetic flux density;
E - irradiance;
D - electric displacement field.

Please, have a look at these equations. Are they correct?
I can't grasp the idea. Any explanations?
I need some intuitive understanding of this formulas (if they are correct) and some knowledge about how they are derived...

I will be grateful for every comment...

Wish you everybody a nice day!

 

[Ibix]

Three of these formulas have infinitesimals on one side only. Coupled with your other two threads, they mean you need a better textbook.

 

[DesertFox]

Three of these formulas have infinitesimals on one side only. Coupled with your other two threads, they mean you need a better textbook.

"Three of these formulas have infinitesimals on one side only."
All of these formulas have infinitesimals on both of the sides... d - for infinitesimals.
Could you be more specific about "the three formulas with infinitesimals on one side only"?
Thank you!

 

[Ibix]

dH is infinitesimal. dl/dt is not infinitesimal.

As I asked you on your breaking strain thread, please provide a reference. This is either nonsense or there is a lot of context I'm missing.

 

[DesertFox]

dH is infinitesimal. dl/dt is not infinitesimal.

As I asked you on your breaking strain thread, please provide a reference. This is either nonsense or there is a lot of context I'm missing.

I am translating the text. But that is all the context! He is expressing relationship between, for example, H (magnetic field strength) and dl/dt (which is related to "wave")... and that is all, believe me! His book is compilation of short fragments (numbered 1, 2, 3...) and he is really brief... that's why everything is so mysterious and puzzling. So, please, if you have any ideas what can be- help me. People in this forum have much more knowledge in Physics than me- i am not arguing...

 

[DesertFox]

There is no more context!
The only clue: dl, dt and dx have something to do with WAVE.

 

[Ibix]

As I pointed out in the other thread, PF rules require you to provide a reference when asked. Please do so.

 

[DesertFox]

As I pointed out in the other thread, PF rules require you to provide a reference when asked. Please do so.

Jordan Metodiev, Bulgarian author (engineer, philosopher, writer), "Philosophical Tractate on Physics" (2014),
I can give link to the original text, but it is not in English.

I hope this information (proper reference) will be useful for finding answer to my questions.
The full context is translated by me and it contains in my questions (in my threads).
Thank you!

 

[Ibix]

If it's online, please link. I'm not going to buy a book, but maths is maths.

 

[DesertFox]

But my suggestions is: let's discuss concepts, ideas formulas... not the author, not the proper reference, not the PF rules... but concepts, ideas, formulas.

I do my best to ask my question clearly, providing all the context which I have. If something in my post is not clear- I can try to make it even more clear.
That's not the issue.

If it's online, please link. I'm not going to buy a book, but maths is maths.

Here it is, for example, the whole fifth fragment! This is the original text without translation:

5.

dH =dl/dt; dB = μodH = dl/dx; dE/dB = - dx/dt; dE = dl/dt; dD = εodE = dl/dx; dH/dD = - dx/dt.

Физичната вълна се "улавя" в т. нар. магнитоелектрично полеФарадей: dE/dB = - dx/dt; B/H = μo (дефинитивно);Максуеловата добавка към Ампер: dH/dD = - dx/dt; D/E = εo (дефинитивно);E, H - вектор на електричната и вектор на магнитната напрегнатост;

D, B - вектор на електричната и вектор на магнитната плътност;

x ┴ t ┴ dx/dt - пространствената координата, времевата координата и

скоростта на разпространение (времепространствената причинност); т. е. тук става

въпрос за онагледяване (символична стереометрия) на вълновата аналитика (скорост

на разпространение в пространство-времето), като едното от пространствените

измерения е отделено въобще за пространството... Бездарието подменя

действителността с... фактология. Математическият език (спрямо музикалния) има

това незаменимо аналитическо предимство, щото да разделя компонентите на

достатъчното основание, а именно: времето, пространството и причинността и да

координира анализа; и невям в "синтетическа употреба" (палиативът на

творчеството) се изразява "порокът" на математическия изказ: фабрикува се во

истине факто-логия, за която възвратно да се твърди, че е "математически

моделирана". И ето как битието се сдобива "свише" със субстанциалност, т. е. твърд,

сиреч устой; за да могат бездарниците, щъкайки, да не си знаят мястото... Това,

което на философа липсва у едно строго фактологическо изложение, е тълкуванието

(нямам предвид бабините деветини); предозираните факти убиват боговете и раждат

философите... И ето че теорията на относителността иде не само да детронира т. нар.

абсолют, но и да предложи живеца... εo, μo - електричната и магнитната вакуумна

проницаемост.(A) dE/dx = - dB/dt;

d/dx(dE/dx) = - d/dx(dB/dt);

d2E/dx2 = - d/dt(dB/dx) = - μod/dt(dH/dx);

d2E/dx2 = εoμod2E/dt2. (dH/dx = - dD/dt; dD = εodE.)(B) dH/dx = - dD/dt;

d/dx(dH/dx) = - d/dx(dD/dt);

d2H/dx2 = - d/dt(dD/dx) = - εod/dt(dE/dx);

d2B/dx2 = εoμod2B/dt2. (dH = dB/μo; dE/dx = - dB/dt.)

(A + B) d²(E+B)/dx² = [√(εoμo)]²[d²(E+B)/dt²].

 

[Ibix]

Get a better textbook.

He's got the infinitesimal equal to something finite problem I already pointed out.

If you combine his first and fourth equations (which are wrong, see above) then he says E=H.

The Faraday-Maxwell equation says that $$\nabla\times \vec E=-\frac {\partial \vec B}{\partial t} $$In the specific case of an electric field pointing perpendicular to the x direction this reduces to $dE/dx=-\partial B/\partial t$. He says that this special case is a definition, which seems to lack context at best. He also simply ignores the "partial" bit of the partial differential with no justification. Then he writes $dE/dB=-dx/dt$. Um.

And finally his last equation adds together two quantities (E and B) which have different units. No.

Get another textbook. Any other textbook.

 

[Vanadium 50]

let's discuss concepts

Fair enough. What you've posted is gibberish. (Infinitesmal on one side)

 

[Ibix]

But my suggestions is: let's discuss concepts, ideas formulas... not the author, not the proper reference, not the PF rules

Just to add: the reason academics - not just PF - require references is so that we can sort out what you say from what the original author said. It's a matter of intellectual honesty to do your best to be clear about where information comes from, and whose work you are relying on. It makes it easier to stop mistakes spreading and to localise them when they do.

In this case it is helpful to have seen the original text because I'm now convinced it's a poor one. It's not you having difficulty understanding; it's the text you're trying to understand. Learn from another source.

 

[Dale]

This is not a good source. You should immediately stop trying to understand it and instead spend your time trying to understand a standard high quality textbook. We cannot help you other than to point out that the source is bad.

 

[DesertFox]

Fair enough. What you've posted is gibberish. (Infinitesmal on one side)

Let's have a look at the first equation: dH=dl/dt
We have inifinitesimal on the left side, OK. But dl/dt can be regarded (and treated as!) as inifinitesimal, too. I can't understand what is the problem with that.
Excuse me for my tenacity.. I can't understand your specific critique...

 

[weirdoguy]

But dl/dt can be regarded (and treated as!) as inifinitesimal, too.

How?

 

[DesertFox]

How?

How? Call it a priori. Call it imagination.
Mathematics are not postulate from God, they are instrument (device) of our human thinking.

 

[weirdoguy]

Yes, and those instruments don't work the way you claim they do. Please provide reference for what you said.

 

[DesertFox]

Yes, and those instruments don't work the way you claim they do. Please provide reference for what you said.

How can i provide you reference for the fact that 1+1=2 ?
infinitesimal / infinitesimal gives you infinitesimal, it is simple like this.

 

[weirdoguy]

It's simply not true. You don't understand how infinitesimals work.

 

[DesertFox]

It's simply not true. You don't understand how infinitesimals work.

OK, guys! I give up! I feel stupid...
You want to tell you the truth? I am just a stupid bulgarian lawyer, who loves Philosophy and Physics. And Physics is my new love, and I am trying to gain some knowledge and groundings...
But obviously, this forum is not the place for me, and Physics is not my thing. And I am poor mathematician, I admit the fact.

Excuse my registering in the forum. I was not trying to offend anybody, I swear.

 

[Ibix]

You are going to need to study calculus if you want to understand physics in any depth. Loosely, though, the d means an infintesimally small change in whatever. So dH is an infintesimally small change in H. dl is an infinitesimal change in l and dt is an infinitesimal change in t. But dl/dt is the rate of change of l with t - it's a finite quantity. If you draw a graph of l as a function of t it's the slope of the line. It's not infinitesimal (loosely speaking the "infinitely smalls" cancel out). So it cannot be equal to dH.

Please get a decent textbook. This one is failing you badly.

 

[Drakkith]

You want to tell you the truth? I am just a stupid bulgarian lawyer, who loves Philosophy and Physics.

If you made it through law school then I doubt you are stupid. I certainly could never hope to study law. It's just not my thing.

 

[davenn]

OK, guys! I give up! I feel stupid...
You want to tell you the truth? I am just a stupid bulgarian lawyer, who loves Philosophy and Physics. And Physics is my new love, and I am trying to gain some knowledge and groundings...
But obviously, this forum is not the place for me, and Physics is not my thing. And I am poor mathematician, I admit the fact.

Excuse my registering in the forum. I was not trying to offend anybody, I swear.

you are not stupid and you haven't offended anyone

and the Physics Forums is the IDEAL place for your to learn new physics concepts

the people here are just trying to get you to see that you are being led astray with a bad book and teaching
you just have to get that out of your system and stop referring to it.

I am sure people here could suggest some excellent basic and intermediate level university textbooks that would get you going in the right direction

above all else DONT GIVE UP ... just be prepared to listen and learn from good advice from the awesome people on this forum cheers
Dave

 

[Dale]

It's simply not true. You don't understand how infinitesimals work.

Quite possibly from reading other material of a similar quality

@DesertFox do not feel bad about being led astray by a bad source. You were savvy enough to recognize there was something off. So we are telling you that what was off was not your comprehension, but rather the source.

 

[DesertFox]

You are going to need to study calculus if you want to understand physics in any depth. Loosely, though, the d means an infintesimally small change in whatever. So dH is an infintesimally small change in H. dl is an infinitesimal change in l and dt is an infinitesimal change in t. But dl/dt is the rate of change of l with t - it's a finite quantity. If you draw a graph of l as a function of t it's the slope of the line. It's not infinitesimal (loosely speaking the "infinitely smalls" cancel out). So it cannot be equal to dH.

Please get a decent textbook. This one is failing you badly.

In other words, I would like to ask: does an infinitesimal change in D (electric displacement field) change the rate of change of l with x ?

If the answer is YES, can you, please, write the correct mathematical expression of this?

 

[Ibix]

He never explicitly defined l. He defined it implicitly to be two different things, but using equations that make no sense. He provides no explanation for that list of expressions at the top of the chapter. I literally have no idea what he was trying to express there so I have no idea what the correct expression is.

I'm not going to answer more questions about this book. It is pure nonsense and discussing it is a waste of my time. It's a waste of yours, too, and I'm sorry that you seem unable to accept this.

Maxwell's equations are $$\begin {eqnarray*}
\nabla\vec E&=&\frac \rho {\epsilon_0}\\
\nabla\times\vec E &=&-\frac {\partial \vec B}{\partial t}\\
\nabla\vec B&=&0\\
\nabla\times\vec B&=&\mu_0\left (\vec J+\epsilon_0 \frac {\partial\vec E}{\partial t}\right)
\end {eqnarray*} $$
The $\vec D$ and $\vec H$ fields are the same as the $\vec E$ and $\vec B$ fields in vacuum. They're different inside materials.

You will be able to find a proper discussion of the electromagnetic wave equation online. But you are going to have to learn some calculus from a reliable source. You might want to check reading lists of physics courses in Bulgarian universities for decent Bulgarian language sources.

 

[DesertFox]

He never explicitly defined l.

His starting point is the wave equation: d²l/dx² = (1/k²)(d²l/dt²)
In this equation l is explicitly defined.

According to me, he is trying to express that an infinitesimal change in D (electric displacement field) leads to a change in the rate of change of l with x.
Or this doesn't make sense?

 

[Ibix]

Or this doesn't make sense?

I'm not going to answer more questions about this book. It is pure nonsense and discussing it is a waste of my time. It's a waste of yours, too, and I'm sorry that you seem unable to accept this.

 

[Mark44]

dH=dl/dt
dB=dl/dx
dE/dB=-dx/dt
dD=dl/dx
dH/dD=-dx/dt

<snip>

Please, have a look at these equations. Are they correct?

The first, second, and fourth equations are NOT correct, as has already been pointed out in this thread.

Jordan Metodiev, Bulgarian author (engineer, philosopher, writer), "Philosophical Tractate on Physics" (2014),

But Metodiev doesn't list mathematician or physicist in his background. Do yourself a favor and toss this book into the trash. I would imagine that some philosophers understand physics, but Metodiev doesn't.

Let's have a look at the first equation: dH=dl/dt
We have inifinitesimal on the left side, OK. But dl/dt can be regarded (and treated as!) as inifinitesimal, too.

No. dl/dt is not an infinitesimal - it is a derivative, the rate of change of I (current in amperes) with respect to time. At least I think you wrote the letter 'I' ("eye") rather than 'l' (lower-case "ell").

I can't understand what is the problem with that.