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Old Jul 10th 2017, 10:46 PM   #1
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D (electric displacement field)

Hello, guys!!

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?
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Old Jul 16th 2017, 10:25 PM   #2
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Originally Posted by DesertFox View Post
Hello, guys!!

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?
First I'd like to make you aware of the other name that D is referred to in the physics literature, i.e. Electric Flux Density. In some texts D is not given a special name but merely referred to as an auxiliary field.

Now, regarding your question, it doesn't make any sense to me. In the first place you didn't define the terms that you used, i.e. what are the quantities l with x. Since you didn't define them I'll have to guess what they are.

I'll assume that l is current and x is the position vector. Is that correct? If so then I don't see a direction relationship between these quantities as a general rule. For example: let's say we have a material which is, in all generality represented by a non-linear combination of the components of the electric field. The problem with your question is you wrote

"infinitesimal change in D" without telling us whether its a change due to an infinitesimal change in time or an infinitesimal change in position.
Nor did you mention the same thing with respect to the current.

If you meant does the change in D in position change dI/dx then the answer is not well defined since it will depend on the exact situation. This is because there can be a non-zero D with no current present at all such as an EM wave in space. Or you can have a current in a material which has a non-linear relationship between D and E. But I see no relationship between that and dI/dx whatsoever.

So your question makes no sense to me. Why do you ask?
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Old Jul 16th 2017, 10:46 PM   #3
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I was reading an article by Bulgarian author. I saw in the text the following equation: dD=dl/dx

That's why I asked my question... I just can't understand what this formulation means.... I can't grasp the idea.

The quantities l (small L) and x are defined (in our context) by the famous wave equation: dl/dx = (1/k)(dl/dt)

So, please, if you have any idea, help me to understand this: dD=dl/dx

I will appreciate every comment!
Best regards!!!!
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Old Jul 16th 2017, 11:19 PM   #4
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Originally Posted by DesertFox View Post
I was reading an article by Bulgarian author. I saw in the text the following equation: dD=dl/dx

That's why I asked my question... I just can't understand what this formulation means.... I can't grasp the idea.

The quantities l (small L) and x are defined (in our context) by the famous wave equation: dl/dx = (1/k)(dl/dt)

So, please, if you have any idea, help me to understand this: dD=dl/dx

I will appreciate every comment!
Best regards!!!!
Yuck! It's difficult to say unless you can tell me the exact name of the author and the exact name of the text so that I can look it up myself.

In general you can't take the derivative of a vector with respect to a vector. It's an undefined operation. The symbols used in that expression have a very specific and are very rarely used. I know that I've seen the operator d before but I just can't recall where I saw it or its definition and I can't find it in any of the many EM texts I have. Yeesh! This kind of thing could keep me up all night or drive me crazy, which ever comes first.

Last edited by Pmb; Jul 17th 2017 at 12:04 AM.
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Old Jul 17th 2017, 10:52 PM   #5
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He is using D for infinitisimal change....
But I think, in that context, dD=dl/dx is wrong mathematical expression, because we have infinitisimal only on the left side and dl/dx expresses rate.

But this is just my suggestion. I am not even good at Mathematics....
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Old Jul 18th 2017, 05:14 AM   #6
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If you'd like my opinion - Get rid of that text now. Nothing good can come from trying to understand a terribly written text when there are so many wonderfully written texts out there. Clearly you can understand English so here's my advice on a text. Get the EM text written by David Griffths. It's awesome.
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