The origin of an \(x\) axis is placed at the center of a nonconducting solid sphere of radius \(R\) that carries a charge \(q_{\text {sphere }}\) distributed uniformly throughout its volume. A particle that carries an unknown charge \(q_{\text {part }}\) is located on the \(x\) axis at \(x=+2 R\). The magnitude of the electric field due to the sphere-particle combination is zero at \(x=+R / 4\) on the \(x\) axis.

(a) What is \(q_{\text {part }}\) in terms of \(q_{\text {sphere }}\) ?

(b) At what other locations on the \(x\) axis is the electric field zero?