Coulomb's law in its vector form?

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Discussion Overview

The discussion revolves around the vector form of Coulomb's law, particularly focusing on the directionality of the force between charges and the concept of charge density. Participants explore how to express these concepts mathematically and clarify their understanding of the underlying principles.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note the importance of direction in the force vector ##\vec F##, especially when charges are of opposite signs, which can affect the direction of the force relative to the position vector ##\vec r##.
  • There is a discussion about the expression of charge density, with a participant questioning whether charge density can be negative, which could simplify the expression of direction.
  • One participant suggests that the lack of absolute symbols in the formula makes it easier to express direction.
  • Another participant confirms that charge density can indeed be negative, linking it to the presence of negative charges.

Areas of Agreement / Disagreement

Participants generally agree on the concept that charge density can be negative and that this affects the directionality of the force vector. However, there is no consensus on the best way to express these concepts mathematically, as some participants express confusion about the notation and representation.

Contextual Notes

There are limitations in the discussion regarding the clarity of mathematical expressions and the use of LaTeX for formulas, which some participants find challenging. The discussion also reflects varying levels of familiarity with the concepts being discussed.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to understand the vector form of Coulomb's law, particularly in relation to force direction and charge density concepts.

ConfusedRookie
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sorry I have use the image I made. Since I don't know how to perform the formula on forum :(
This is the problem I am having.
wtf12345.png
 
Last edited:
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Hello Rookie, :welcome:

You would miss the direction of ##\vec F## if one of the two charges has a charge opposite to the other...
In other words: ##\vec F## can be in the same direction as ##\vec r## or it can be in the opposite direction.
 
suggest2.png
 
BvU said:
Hello Rookie, :welcome:

You would miss the direction of ##\vec F## if one of the two charges has a charge opposite to the other...
In other words: ##\vec F## can be in the same direction as ##\vec r## or it can be in the opposite direction.
Oh my god. I've just realized without the absolute symbols. It would be more easier to express the direction. Oh my oh my thank you very much teacher :)
 
My pleasure
 
BvU said:
My pleasure
Teacher. There's one more thing I would like to ask. I see there are many formula using "charge density". Is charge density able to be negative !?

ae544e.gif


If a charge density can be negative, it is very much easy to express its direction. I didn't find any vector form E that use the unit vector to express direction. They mainly focus on the magnitude.
 
With ##\vec F = q\vec E\ ## you can use (almost) the same expression

Charge density can be negative, yes: negative charge leads to negative charge density :smile:

Your picture in post #6 comes through as a lot of letters/numbers :nb)
 
ConfusedRookie said:
Since I don't know how to perform the formula on forum :(
Click HELP at the bottom of any page and then LaTeX Primer.
 

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