You are designing a new guidance mechanism for an inkjet printer. You believe that a circular arc of charge, mounted in the \(x y\) plane, is needed in order to deflect the ink droplets most efficiently from their original path along the \(z\) axis. You want to use a uniformly charged arc of arc length \(s\) that subtends an angle \(2 \theta\) along a circle of radius \(R\) through whose center the ink droplets will pass. The amount of charge that can easily be transferred to the arc is \(q\), which limits the magnitude of the electric field that can be attained at the center of the circle.