Current?

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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