A small sphere whose mass m is 1.12 mg carries a charge . It hangs in the Earth’s gravitational field from a silk thread that makes an angle with a large uniformly charged nonconducting sheet as shown in the figure. We have to calculate the uniform charge density for the sheet.

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We will draw the free-body diagram of forces acting on the charged sphere of mass m carrying charge q in the electric field produced by a large nonconducting sheet with charge density .

It is given that at equilibrium the string with which the spherical ball has been suspended is at an inclination with respect to the vertical. Angle of inclination is

.

Electric field due to a large sheet having charge density will be perpendicular to the sheet and its magnitude will be

.

Resolving the forces acting on the charged sphere in the horizontal and vertical directions and requiring that at equilibrium the net components will be zero, we get

,

and

.

It is given that

.

Therefore,

We therefore find