- #1
Coulomb's law and Electric field intensity problem
- Thread starter rizwanibn
- Start date
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Discussion Overview
The discussion revolves around a problem related to Coulomb's law and electric field intensity, focusing on a specific question from a textbook. Participants are attempting to resolve discrepancies between their calculations and the textbook answer, exploring various mathematical approaches and interpretations.
Discussion Character
- Homework-related
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant expresses difficulty in obtaining the textbook answer and seeks assistance.
- Another participant cautions about the absolute value signs in the inequality, suggesting a specific interpretation of the conditions.
- A participant proposes that the integration volume should consist of eight small cubes, providing a geometric illustration to clarify their reasoning.
- There is a suggestion that the arrangement of cubes leads to cancellation of electric field contributions due to opposite signs.
- A later reply emphasizes the need for calculations to verify the claims about cancellation.
Areas of Agreement / Disagreement
Participants do not reach a consensus, as there are multiple interpretations of the problem and differing opinions on the correct approach to the calculations.
Contextual Notes
Some assumptions regarding the integration volume and the interpretation of inequalities remain unresolved. The discussion highlights potential dependencies on definitions and the need for careful mathematical handling.
- #2
blue_leaf77
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Be carefull with the absolute sign in the inequality. ##0.1 \leq |x| \leq 0.2 = (x\leq -0.1 \cup x\geq 0.1) \cap -0.2\leq x \leq 0.2##.
- #3
- #4
- #5
blue_leaf77
Science Advisor
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Yes, I think that should give you the correct answer.
- #6
rizwanibn
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Is it addition of subtraction in between...?
- #7
blue_leaf77
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On a second thought, I think your the integration volume should be eight small cubes of sides 0.1 at each corner of a large cube of sides 0.4. As illustration for x-y plane, see picture below. The intersection area in that picture actually forms four long bar of square cross section when put in a 3D coordinate. If you add the last region corresponding to the inequality for ##z##, you should get 8 cubes as the integration volume.
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- #8
rizwanibn
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Thanks very much.
Got a very good understanding of it.
So all the cubes has a pair of opposite sign and they cancel out each other.
Got a very good understanding of it.
So all the cubes has a pair of opposite sign and they cancel out each other.
- #9
blue_leaf77
Science Advisor
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You have to do the calculation to see if that's true.
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