One end of a 10 cm long silk thread is fixed to a large vertical surface of a charged non conducting plate and the other end is fastened to a small ball having a mass of 10 g and charge of `4.0 xx 10^ C`. In equilibrium, the thread make an angle of `60^0` with the vertical. Find the surface charge density on the plate.

Explanation

To solve the problem step by step, we will analyze the forces acting on the charged ball and apply the principles of equilibrium and Gauss's law.

### Step 1: Analyze the Forces Acting on the Ball
In equilibrium, the forces acting on the ball are:
1. The gravitational force (weight) acting downwards: \( F_g = mg \)
2. The tension in the thread acting at an angle of \( 60^\circ \) with the vertical: \( T \)
3. The electrostatic force due to the electric field created by the charged plate: \( F_e = QE \)

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