A small bob of mass 100 mg and charge +10 μ C is connected to an insulating string of length 1 m. It is brought near to an infinitely long…

A small bob of mass $\displaystyle 100$ mg and charge $\displaystyle +10 \mu \mathrm{C}$ is connected to an insulating string of length $\displaystyle 1$ m . It is brought near to an infinitely long non-conducting sheet of charge density ' $\displaystyle \sigma$ ' as shown in figure. If string subtends an angle of $\displaystyle 45^{\circ}$ with the sheet at equilibrium the charge density of sheet will be. (Given, $\displaystyle \epsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}$ and acceleration due to gravity, $\displaystyle \mathrm{g}=10 \frac{\mathrm{~m}}{\mathrm{~s}^2}$ )