Dl (dot) r hat in computing potential?

AI Thread Summary
The discussion focuses on the correct approach to computing the line integral of electric potential from infinity toward a charge. It emphasizes that while the direction of the integral points toward the charge, the vector r hat points away, leading to confusion about the sign. The proper method involves using negative r hat for the vector dl to ensure the potential is calculated correctly. It is highlighted that reversing the sign of dr is a common mistake, and the integration limits should be set from "far" to "near" to maintain the correct sign. This ensures accurate computation of the electric potential.
platonic
Messages
38
Reaction score
0
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...?
 

Attachments

  • p0097.jpg
    p0097.jpg
    22.7 KB · Views: 677
  • p0098.jpg
    p0098.jpg
    32.2 KB · Views: 533
Physics news on Phys.org


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
 
Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
Back
Top