This is a question I read in an article that discusses about misconception of physics among students.
they only provided the question and some of the wrong principles students suggested.
Three Points , located on the vertices(vertexes) of an equilateral triangle and have potentials 0V, 50 V ,-25V as in the figure I attached to this thread.
The students were asked to sketch electric field lines and equipotential surfaces.
Electric field line's starting point should be either a charge or infinity.
Electric field line's ending point should be either a charge or infinity.
the misconception was that students sketched electric field lines from one point to another as if there were charges there.
The Attempt at a Solution
First, I assumed they are apart distance d from each other.
then I divided the question into 3 two-pairs and found the electrical field that should be in a specific direction to satisfy this voltage difference.
the pair P2 -P1 has potential difference of 50V thus I can assume there is an electric field in the direction from P2 to P1 with magnitude of 50/d (but not starting from point P2, it starts from infinity ,just the direction is... you could say 30 degrees wit the vertical.)
then I summed all the components to find the direction of the "net Electric Field" which happens to be 19.1 degrees(if I'm not mistaken) to the left of the vertical as shown in the second diagram,and the direction is independent of d.
and about the equipotential surfaces,
IMO they are perpendicular to the electric field lines but they are not really surfaces :S just lines, and I'm not sure if it's OK ( they are infinte so I can say the are surfaces ??).
anyway,any suggestions and help is appreciated, I've never been that in-secure in a physics question.