A thin, flat plate shaped as a sector of a circle of radius \(R\) lies in the \(xy\)-plane with its vertex at the origin \(O\). The sector subtends an angle \(\theta_0\) symmetric about the positive \(x\)-axis, spanning from \(\theta = -\theta_0/2\) to \(\theta = +\theta_0/2\). The plate carries a non-uniform surface charge density given by \(\sigma(r) = \sigma_0 \left(\dfrac{r}{R}\right)\), where \(\sigma_0\) is a positive constant and \(r\) is the radial distance from the origin. In terms of \(\sigma_0\), \(\theta_0\), and physical constants, what is the magnitude of the electric field at the origin \(O\)?