Particle 1 carrying charge \(+q_{1}\) is placed on the \(x\) axis at \(x=-d\). Particle 2 carrying some unknown charge \(q_{2}\) is placed somewhere on the \(x\) axis. The potential energy associated with the charges is \(+q_{1}^{2} /\left(2 \pi \epsilon_{0} d\right)\), and the electrostatic potential due to the charges is \(+q_{1} /\left(\pi \epsilon_{0} d\right)\) at the origin and zero at an infinite distance.

(a) What is the sign of the charge on particle 2?

(b) What is the magnitude of the charge on particle 2 , and where on the \(x\) axis was particle 2 placed? Determine all possible answers.