Five charged particles are located around a semicircular arc of radius \(100 \mathrm{~mm}\), with one particle at each end of the semicircle and the remaining three spaced equally between the two ends. The semicircle lies in the region \(x<0\) of an \(x y\) plane, such that the complete circle is centered on the origin.

(a) If each particle carries a charge of \(1.00 \mathrm{nC}\), what is the electric field at the origin?

(b) Where could you put a single particle carrying a charge of \(-5.00 \mathrm{nC}\) to make the electric field magnitude zero at the origin?