An infinitely long positively charged wire with a uniform linear charge density \(+\lambda\) is parallel to the \(y\) axis of a Cartesian coordinate system and passes through the \(x\) axis at \(x=-d\). At the origin, the electric field due to this charged wire has magnitude \(E_{0}\) and is directed to the right along the positive \(x\) axis. A second infinite charged wire, parallel to the first and with a uniform linear charge density, passes through the \(x\) axis at \(x=+3 d\). The vector sum of the electric field at the origin due to the two lines of charge has magnitude \(2 E_{0}\). What is the linear charge density of the second charged wire? Obtain all the possible answers.