Two infinitely wide charged plates carry opposite charge densities of magnitude \(1.77 \times 10^{-6} \mathrm{C} / \mathrm{m}^{2}\). A small sphere, of mass \(\mathrm{m}=2 \mathrm{~g}\), lies between the plates, attached to the positive charged plate by means of an inextensible insulating wire of negligible mass. At equilibrium, the wire forms an angle of \(30^{\circ}\) with respect to the positively charged plate. Find the magnitude of the charge on the sphere.