The value of q if it floats in air is

The magnitude of electric field due to the charged conducting plate is E = $\frac{\sigma}{\varepsilon_r}$

As the charged particle is floating in air (neglecting the buoyant force due to air we obtain)

mg = qE

$\Rightarrow q=\frac{m g}{E}$

$\Rightarrow q=\frac{m g \varepsilon_r}{\sigma}$

∴ (A)