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
Answer & explanation
Correct answer: option 1
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$
$\Rightarrow tan\beta = \frac {q\sigma}{\epsilon_0 mg}$
$\sigma \propto tan\beta$