There is one large vertical non-conducting plane surface with uniformly distributed charge. A pendulum bob is suspended through an insulating string from a point on this non-conducting surface. The length of the string is l and mass of the bob is m. The charge carried by the pendulum bob is q. It is found that in a state of equilibrium, the string of the pendulum makes `60^@` angle with the vertical. What will be the charge per unit area on surface? Also calculate the tension developed in the string in equilibrium state.

Explanation

To solve the problem step by step, we will analyze the forces acting on the pendulum bob and derive the required expressions.

### Step 1: Identify the Forces Acting on the Pendulum Bob
The pendulum bob experiences three forces:
1. The gravitational force \( \vec{F_g} = mg \) acting downward.
2. The electric force \( \vec{F_e} = qE \) acting horizontally due to the electric field generated by the charged plane surface.
3. The tension \( \vec{T} \) in the string acting along the string.

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