An infinitely long positively charged wire that carries a uniform linear charge density \(\lambda\) passes through the origin of an \(x y\) coordinate system and lies on the \(y\) axis. At the position \(x=d\) on the \(x\) axis, the electric field created by this wire has magnitude \(E\) and is directed to the right along the positive \(x\) axis. A charged particle is then placed on the \(x\) axis at \(x=2 d\). At \(x=d\) on the \(x\) axis, the electric field created by this particle has magnitude \(2 E\) and is directed to the left along the \(x\) axis.

(a) At what positions on the \(x\) axis is the vector sum of the electric fields zero? 

(b) What is the magnitude of the electric field produced by the wire at the locations you identified in part \(a\) ?