A particle, carrying a positive charge of \(4 \mathrm{nC}\), located at \((5 \mathrm{~cm}, 0)\) on the \(x\)-axis experiences an attractive force of magnitude 115.2 \(\mathrm{N}\) due to an unknown charge \(q\) located at the origin.

(a) Determine the value of \(q\).

(b) Using the relationship between electric field and electric force and the result from part \((a)\), determine the magnitude and direction of the electric field due to the charge \(q\) at a point located \(20 \mathrm{~cm}\) away from the \(4-\mathrm{nC}\) charge in a direction perpendicular to the line between the two charges.