Dl (dot) r hat in computing potential?

[platonic]

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...?

 

[rcgldr]

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.

 

[platonic]

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??

 

[Gordianus]

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

 

[PJC01]

In computing potential, it is important to consider the direction of the line integral and the direction of the r hat vector. When computing the line integral from infinity back toward a charge, the direction is pointing towards the circle. However, the r hat vector is pointing away from the circle. Therefore, it is necessary to adjust the direction of the vector dl to be in the opposite direction of r hat, which would result in a negative sign for the potential. This adjustment is necessary to ensure that the direction of the line integral aligns with the direction of the r hat vector, as they both represent the direction of the electric field. By taking into account the direction of both the line integral and the r hat vector, we can accurately compute the potential in a given system.