Magnetism Series #7

A conducting ball of radius $3r$ having charge $Q$ is at a great distance from a neutral conducting ball of radius $r$ .
They are connected with a thin perfectly conducting wire of inductance $L$ through a switch.
What will the maximum current in the wire be after the switch is closed?
Answer comes in the form of $I_{max}=\alpha Q \sqrt{\frac{1}{\epsilon_{0} LR}}$

Type your answer as $\alpha=?$

The problem is taken from my Physics Book.