Never mind I just got the answer. It's quite an interesting method mind you.
Hey I've been having a lot of trouble with a question involving the calculating the potential difference between two points.
So I have the following equations for Electric field:
Where x and y are coordinates that are given to me and I have to find the potential difference between (0, 0) and (x, y).
So I know that
But I don't know how to evaluate that "line integral" basically. Also what is my dl???
In the meantime, for those too enthralled to wait, let me guess at the main results: ......
You realised that the electric field was conservative (by checking whether ) and therefore:
1. Could be expressed in the form , and
2. Is independent of the path between the two points.
Then you got and hence found that .
The details will be of interest to others.
Ok here is the long and drawn out method (that actually just gives the same result as Mr. Fantastic got.):
It's a long and drawn out method that but it can be adapted to include the z axis as well as from different points. The challenge is just getting the right position vector.