A small bob of mass 100 mg and charge $ + 10\mu C$ is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density '$\sigma$' as shown in figure. If string subtends an angle of ${45^\circ}$ with the sheet at equilibrium the charge density of sheet will be.
(Given, ${_0} = 8.85 \times {10^{ - 12}}\frac{F}{m}$ and acceleration due to gravity, $g = 10\frac{m}{{{s^2}}}$)