Three narrow concentric rings of radii \(50 \mathrm{~mm}, 70 \mathrm{~mm}\), and \(90 \mathrm{~mm}\) are centered about the origin, with the axis of symmetry of each ring oriented along the \(y\) axis. The charge on the inner ring is \(1.0 \mu \mathrm{C}\), that on the middle ring is \(-2.0 \mu \mathrm{C}\), and that on the outer ring is \(1.0 \mu \mathrm{C}\).

(a) What is the electric field magnitude at \((0,100 \mathrm{~mm}, 0)\) ?

(b) What quantity of charge must be placed at \((0,-100 \mathrm{~mm}, 0)\) to make the electric field magnitude zero at the position calculated in part \(a\) ?