Electric Force of Attraction.

It is known that an electrified body can attract uncharged bodies. For example, a charged comb attracts uncharged pieces of paper.

One can estimate the force of such an interaction between charged and uncharged bodies. For the estimation, consider an electrified body localized at point $A$ with charge $q$ —as shown in the diagram (not drawn to scale)—and an uncharged body in the form of a conducting cylinder whose radius $R$ and the length $l$ are considerably smaller than the distance $a$ from charge $q$ $($ i.e. $a \gg l)$ . The axis of the cylinder passes through point $A,$ and the volume of the cylinder is $V.$

If the force of interaction between them is $\displaystyle \frac { V{ q }^{ 2 } }{ \alpha { \pi }^{ 2 }{ \varepsilon }_{ 0 }{ a }^{ 5 } },$ find the value of $\alpha.$

Assume that no charge appears on the curved surface of the cylinder, provided the length of the cylinder is much smaller than its diameter.