boundaryConditionCil = {
  DirichletCondition[V[r, p] == V0, r == R && 0 < p < Pi/4],
  DirichletCondition[V[r, p] == V0, r == R && 7/4 Pi < p < 2 Pi],
  DirichletCondition[V[r, p] == V1, r == R && 3/4 Pi < p < 5/4 Pi]
  }

If you use these boundary conditions you get:

Plot3D[solCyl[Sqrt[x^2 + y^2], ArcTan[x, y] + \[Pi]], {x, -1,  1}, {y, -1, 1}, ColorFunction -> "TemperatureMap", BoxRatios -> {1, 1, 1}]

The function looks very straight in the middle with a slope that is nearly constant. It is hard to imagine that the gradient and thus the electric field is attracted so much towards the middle. I suspect there must be something wrong either with the calculation of the electric field or with its coordinate transformations.