What the hell is wrong with this?

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Discussion Overview

The discussion revolves around identifying and correcting mistakes in a set of equations related to vector components, specifically focusing on the signs of terms involving dz and E_z. Participants are analyzing the mathematical expressions and their physical implications, with a particular emphasis on the directionality of vectors in a given context.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that both dz parts in the first equation have the wrong sign due to the anti-clockwise direction, suggesting that the first dz-part should be negative.
  • Another participant challenges this claim, stating that the signs are correct based on the properties of dot products and requests to check the attachment for clarification.
  • A later reply indicates confusion over subscripts and suggests a specific correction to the second term in the last equation, proposing it should be (E2z)(dz).
  • Another participant reiterates that the signs are indeed wrong, explaining that the angle definitions lead to incorrect assumptions about the signs of E_z components in the equations.
  • One participant expresses gratitude for the clarification provided by another, indicating a newfound understanding of the issue.

Areas of Agreement / Disagreement

There is disagreement among participants regarding the correctness of the signs in the equations. Some participants believe the signs are incorrect, while others defend the original expressions as being correct based on their interpretations of vector components.

Contextual Notes

The discussion highlights potential misunderstandings related to vector directionality and the application of trigonometric relationships in determining component signs. The reliance on visual representations in the attachment may also contribute to differing interpretations.

LucasGB
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What the hell is wrong with this?! :)

I just can't spot the mistake! Please see if you can.
 
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Sorry, I forgot the attachment.
 

Attachments

  • Curl.jpg
    Curl.jpg
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In your first equation, both the dz parts have the wrong sign. Remember, you are going anti-clockwise, so the first dz-part moves in the negative z-direction, so it should be negative, not positive. The same (or rather, opposite) goes for the other dz-part at x=0.

EDIT: Don't be fooled by the way the arrows are drawed. If E_z is positive in the second term, then it points backward in comparison to the direction of the path, and will therefore contribute negatively, hence the correct expression is -E_z*dz

Torquil
 


torquil said:
In your first equation, both the dz parts have the wrong sign. Remember, you are going anti-clockwise, so the first dz-part moves in the negative z-direction, so it should be negative, not positive. The same (or rather, opposite) goes for the other dz-part at x=0.

EDIT: Don't be fooled by the way the arrows are drawed. If E_z is positive in the second term, then it points backward in comparison to the direction of the path, and will therefore contribute negatively, hence the correct expression is -E_z*dz

Torquil

But I don't think the signs are wrong. It follows from the properties of dot products. Please check the attachment.
 

Attachments

  • Dot products.jpg
    Dot products.jpg
    16.2 KB · Views: 389


Please check the attachment.
Sorry, LucasGB, this may sound stupid, but yes, please check the attachment.
 


Ich said:
Sorry, LucasGB, this may sound stupid, but yes, please check the attachment.

LOL. Oh my God, these subscripts are driving me crazy!

In the last equation, the second term in the sum must be (E2z)(dz).

I truly hope that's the only obvious mistake we're talking about.
 


No I'm pretty sure the signs are wrong. In your second calculation the error manifests itself like this:

Notice how you have defined your angles. Your first and second equation is correct. But when you write it in terms of the components E_x and E_z you are using the wrong sign for both the E_z's.

E.g. the second term: You have defined the theta angle to be the angle between E_2 and -dz. Therefore |E_2|cos(theta) is -E_{2z}, not E_{2z}. The opposite goes for the other E_z part.

You get the component E_z of a vector E by doing |E|cos(theta) where theta is the angle between the vector and the "positively pointing" z-axis. Your are assuming the opposite for the two parts that are related to z-components.

Torquil
 


That's perfect. I can totally see it now. Thank you very much, torquil, you're the man!

I just learned something new!
 

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