An infinitly long thin-walled dielectric cylinder with radius $R$ is devided into four equal parts. Two opposite sectors carry a uniform charge density $\sigma$, while other two are uncharged.

1 Determine the electric field vectorin two points close to the center: their coordinates are $(x;~0)$ and $(0;~y)$. Assume that $x,y \ll R$.

Axes $OX$ and $OY$ are directed along right angles bisectors (see fig.).