A charged ball 'M' hangs from a silk thread 'S' which makes an angle β, with a large charged conducting sheet 'P' as shown. The surface charge density σ of the sheet is proportional to

tan B

Let T is tension in the string , then at equilibrium along horizontal direction is $ T sin\beta = qE = \frac {q\sigma}{\epsilon_0}$

$ T cos\beta = mg$

$\Rightarrow tan\beta = \frac {q\sigma}{\epsilon_0 mg}$

$\sigma \propto tan\beta$