A ring with radius \(a\), linear charge density \(\lambda\) and mass \(m\) is fixed at its center. An infinite plane passing through the ring, perpendicular to its plane, is a conductor, but it doesn't touch any point of the ring. At a distance \(L\) of the ring's axis, such that \(L>>a\), and distance \(x\) from the plane, such that \(x<<1\) there is a stright line with linear charge density \(\Lambda\) such that it is parallel to the ring's axis. The value of \(\Lambda\) such that generates a current \(i\) at the ring can be written as: \[\dfrac{\alpha mL\epsilon_{0}i}{a\lambda^2 \cdot t}\] Where \(\epsilon_{0}\) is the dielectric constant at void and \(t\) is time, find the value of \(\alpha\)

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