The electric force due to a uniform external electric field causes a torque of magnitude \(10.0 \times 10^{-9} \mathrm{~N} \cdot \mathrm{m}\) on an electric dipole oriented at \(30^{\circ}\) from the direction of the external field. The dipole moment of the dipole is \(8.0 \times 10^{-12} \mathrm{C} \cdot \mathrm{m}\).

(a) What is the magnitude of the external electric field? 

\((b)\) If the two particles that make up the dipole are \(2.5 \mathrm{~mm}\) apart, what is the magnitude of the charge on each particle?