An infinite plane sheet of positive charge has surface charge density `sigma`. A metallic ball of mass `m` and charge `+Q` is attached to a thred and is tied to a point `A` on the sheet `PQ`. The angle `theta` made by the string with plane sheet is in equilibrium is

Options

A. zero
B. `tan^(-1)((Qsigma)/(4epsilon_(0)mg))`
C. `tan^(-1)((Qsigma)/(2epsilon_(0)mg))`
D. `tan^(-1)((Qsigma)/(epsilon_(0)mg))`

Explanation

To solve the problem, we need to analyze the forces acting on the metallic ball attached to the thread and determine the angle θ that it makes with the plane sheet when in equilibrium.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Ball**:
- The ball experiences two main forces:
- The gravitational force (weight) acting downwards: \( F_g = mg \)
- The electric force due to the infinite plane sheet: \( F_e = Q \cdot E \)
...