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