A small bob of mass 100 mg and charge +10 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 '' as shown in figure. If string subtends an angle of 45° with the sheet at equ

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Solution

Q.
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 non-conducting sheet of charge density ' $σ$ ' as shown in figure. If string subtends an angle of 45° with the sheet at equilibrium the charge density of sheet will be:

(Given, $ε_{0} = 8.85 \times 10^{- 12} \frac{F}{m}$ and acceleration due to gravity, $g = 10 m / s^{2}$ ) [2025]

1 0.885 $nC / m^{2}$

2 17.7 $nC / m^{2}$

3 885 $nC / m^{2}$

4 1.77 $nC / m^{2}$

Ans.
(4)

T sin 45° = Eq

T cos 45° = mg

$Eq = mg$

$E = \frac{m g}{q} = \frac{σ}{2 ε_{0}}$

$σ = \frac{2 ε_{0} m g}{q} = 1.77 nC / m^{2}$

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