- #1
Mantella
- 10
- 0
I've been having a problem with the sign of potential. Electric potential as I know it is defined as V = -[itex]\int_{C}\vec{E}\bullet\vec{dl}[/itex] where C is the path from a location defined as zero potential to the location you are measuring the potential at. Now I want to run through this really quick with a simple problem such as the potential of a positive point charge. [itex]\vec{E}[/itex]=[itex]\frac{q\hat{r}}{4\pi\epsilon_{o}\tilde{r}^{2}}[/itex] for a point charge (tilde as an integration variable) and because we are moving in a path from infinity (the point defined as zero potential in this case) to some point r, [itex]\vec{dl}[/itex] should equal -d[itex]\tilde{r}\hat{r}[/itex]. Hence V = [itex]\int^{r}_{∞}E\left(\tilde{r}\right)d\tilde{r}[/itex] = -[itex]\frac{q\hat{r}}{4\pi\epsilon_{o}r}[/itex] which is the negative of what it should be.
What's wrong here? I've wondered for months and gotten unsatisfactory explanations from TAs and professors.
Thanks!
What's wrong here? I've wondered for months and gotten unsatisfactory explanations from TAs and professors.
Thanks!