Two charged particles are placed near the origin of an \(x y z\) coordinate system. Particle 1 carries charge \(+q\) and is on the \(x\) axis at \(x=+d\). Particle 2 carries an unknown charge and is at an unknown location. The magnitude of the electric field at the origin is \(q /\left(2 \pi \epsilon_{0} d^{2}\right)\), and the electrostatic potential at the origin, relative to \(V=0\) at infinity, is \(+3 q /\left(4 \pi \epsilon_{0} d\right)\).

(a) If particle 2 is on the \(x\) axis, what are its charge and location? 

\((b)\) If particle 2 is on the \(y\) axis, what are its charge and location? Determine all possible solutions.