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From MKS to GAUSS system E.M. fields transformations

-MFra-
21-Topaz II

From MKS to GAUSS system E.M. fields transformations

Goodmorning everyone!

Is there anyone  who can fix this little problem?

Thanks a lot.

F. M.

eqtransf.jpg

31 REPLIES 31

Yes it is not a man - it is a competer

10-19-solve-must-be-so.png

What........?????

F.M. wrote:

What........?????

Sorry, what what???

...The answer does not comply with the question ...

LucMeekes
23-Emerald III
(To:-MFra-)

I assume your divergence operator is custom defined by yourself (or else please point me where I can find it in Mathcad). Then it is defined as a variable...

Mathcad provides little to no control on the sequence of variables in the output of symbolic evaluation.

You might get by, when you use the divergence operator as an operator (i.e. as a function). I tried this in Mathcad 11 (with the operator/function 'div' undefined ! 😞

Success!
Luc

-MFra-
21-Topaz II
(To:LucMeekes)

I believed that it was not necessary (required)  to indicate the lower placeholder. In some previous version of mathcad, if I remember right, (I did not check) there was not.

In short, without the lower placeholder, the operator does not work?

Since I have many worksheets that use that operator, I would like to continue to keep it without having to change everything but only the definitions.

LucMeekes
23-Emerald III
(To:-MFra-)

What 'lower placeholder' are you referring to?

I used the ' x f ' out of:

to build the LHS of my second equation. But you can see what the symbolic processor returns as output.

In any case, this is mathematically correct.

I still think you used the divergence symbol (only) as a variable, am I right?

Incidentally, where did you find the divergence symbol?

The DEL" is aa gradient function in Mathcad 15, "cntrl-shift-G".  I haven't found it in Prime

LucMeekes
23-Emerald III
(To:Fred_Kohlhepp)

Ah, Thanks Fred.

It doesn't exist as such in Mathcad 11. I don't have 15 at hand.

If I remember correctly in version 12, it was present.

-MFra-
21-Topaz II
(To:LucMeekes)

I refer to this:

nabla op.jpg

They have impressed  me these results:

eqtransf 1.jpg

I have to check the accuracy of the results.

-MFra-
21-Topaz II
(To:LucMeekes)

....have not found them, I've built myself.

divrotop.jpg

RichardJ
19-Tanzanite
(To:-MFra-)

I'm surprised it let's you delete the placeholders. At any rate, when you do you are left with a variable.

-MFra-
21-Topaz II
(To:RichardJ)

I think that this happens in any computer, not just in my computer!?!?

RichardJ
19-Tanzanite
(To:-MFra-)

I can also delete the placeholders. There is no other operator that allows me to do that though.

Excuse me Mr. Valery, if I insist. But your answer has a darker meaning. I probably disturbed someone? I am not aware. Then?

-MFra-
21-Topaz II
(To:-MFra-)

Thinking about it, with regard to the divergence operator, since I used the dot product, which is commutative (while the vector product is not) the program (considering both arguments as vectors) swaps the operator (seen as a vector) with the vgiven ector. Swapping that is not valid for the vector product.

Werner_E
24-Ruby V
(To:-MFra-)

You are right, that you can omit/delete the placholder for the variable in the gradient operator. But it seems that you deleted the placeholder for the function, too, and so you end up as Richard already stated with a simple variable. You see the multiplication dot between the nabla-symbol and the variable D or B.

I am not sure what you expected the nabla-symbol to be. Mathcad obviously gives you the result you expected anyway as the order of the operands in a product does not matter.

-MFra-
21-Topaz II
(To:Werner_E)

Thanks for the examples. I know what is written in the guide, and I've taken into account.

I use these operators since I was a boy.

The symbol is called nabla and it defines the gradient operator acting on a scalar.

Similarly to what is realized in mathcad for it, I would like to define the other two vector operators with the use of nabla: divergence and rotor that act on vectors.

Werner_E
24-Ruby V
(To:-MFra-)

If you know all what was written already I wonder, why you ask

You should also know that we have in general very few influence on the way Mupad presents its results and how it arranges its variables.

And the nabla symbol the way you used it is just a variable,, not an operator!

-MFra-
21-Topaz II
(To:Werner_E)

... I thought that, despite nabla was considered as a variable, the processor had not swapped the two variables in such a way that the equation formally was correct. As are formally correct the following:

maxw eq.jpg

Werner_E
24-Ruby V
(To:-MFra-)

I see - basically in great parts you are using Mathcad simply as an equation editor, so making nabla a variable does not harm if you connive at the (implicit or explicit) multiplication after the symbol. But when it comes to symbolic math, you run into troubles. While I doubt its a good idea making the nabla operator a varible, may the keyword "collect" helps.

Sometimes you are able to take influence on the outcome that way:

-MFra-
21-Topaz II
(To:Werner_E)

As you can see in the previous  immage, I have formatted nabla as a vectorial operator and not as a simple variable. However, it does not match any operation on vector ..

I like to do the works presentable, who have a "head" and a tail. Throw there, formulas that no one understands, I do not like, then the formulas are necessarily accompanied by text. It seems obvious!

Werner_E
24-Ruby V
(To:-MFra-)

> As you can see in the previous  immage, I have formatted nabla as a vectorial operator and not as a simple variable.

I was not talking about how YOU see the symbol but how Mathcad sees it. If you want Mathcad to see it as a functional operator, you are not allowed to delete the placeholder for the function! Otherwise all you get is a multiplication of a variable (or a vector in case of the vector product) with a function.

-MFra-
21-Topaz II
(To:Werner_E)

alles klar!
Danke.
Tschüss

-MFra-
21-Topaz II
(To:-MFra-)

The answer of Luke Meeks would be fine if I did not want to use nabla. That, however, I will. So far, there is no right answer.

LucMeekes
23-Emerald III
(To:-MFra-)

I think the closest you can get is to use the cross-product operator:

And I find the prefix notation result, with the nabla operator, intriguing.

Success
Luc

LucMeekes
23-Emerald III
(To:LucMeekes)

OK. the nabla symbol is not available in Mathcad 11, but,

using the undocumented symbolic functions Diff() and diff()

that produce respectively calculate (partial) derivatives of

the (assumed function) first parameter to the second parameter:

you can get this:

For those who can benefit from it.

-MFra-
21-Topaz II
(To:LucMeekes)

Mathcad 15 results:

LM-answer.jpg

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