The charged ball b hangs from a silk thread s which makes an angle theta with a large charged conducting sheet p . The surface charge density is proportional to

Cot theta

Cos theta

Tan theta

Sin theta

the strength of the electric field of an infinite plane charge is independent of the distance from the plane, and it is directly proportional to sigma. Let the constant of proportionality be 'k'

k*sigma*cos(theta)=mgsin(theta)

therefore, sigma is proportional to tan(theta)