Dl (dot) r hat in computing potential?

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Discussion Overview

The discussion revolves around the computation of electric potential using line integrals, particularly focusing on the direction of the differential vector dl and its relationship with the unit vector r hat. Participants explore the implications of integrating from infinity towards a charge and the associated signs in the calculations.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions the direction of r hat when computing the line integral, suggesting that it points away from the charge while the integration direction points towards it, leading to a potential sign issue.
  • Another participant provides the definition of potential as the negative of the work done per unit charge, implying a relationship to the line integral being discussed.
  • A different participant asserts that the sign of dr should not be reversed and emphasizes that proper integration limits will inherently account for the correct sign in the calculation.

Areas of Agreement / Disagreement

Participants express differing views on the treatment of the direction of dl and r hat in the context of the line integral, indicating that there is no consensus on the correct approach to take in this computation.

Contextual Notes

The discussion highlights potential misunderstandings regarding the integration limits and the treatment of vector directions in the context of electric potential calculations, but does not resolve these issues.

platonic
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dl (dot) r hat in computing potential??

when computing the line integral "from infinity" back toward charge, the direction is pointing to the circle. But r hat is pointing away from circle. So vector dl should equal magnitude dl times negative r hat, which would change sign of potential...?
 

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Potential is defined to be the negative of the work done per amount of charge of an object by a field when that object in the field moves from one point to another.
 


I know that is the definition of work. But in computing that line integral, shouldn't integrating in from infinity be integrating along the direction of negative r hat??
 


Don't EVER reverse the sign of dr. It's a very common mistake. The proper integration limits take care of the sign. When you move from "far" to "near" the lower integration limit is "far" and the upper "near". This way, you get the right sign
 

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