A small bob of mass 100 mg and charge +10 C is connected to an in… - Vidyadip

MCQ

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 nonconducting 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, $\varepsilon_0=8.85 \times 10^{-12} \frac{F}{ m }$ and acceleration due to gravity, $g =10 m / s ^2$ )

A
$0.885 nC / m ^2$
B
$17.7 nC / m ^2$
C
$885 nC / m ^2$
✓
$1.77 nC / m ^2$

✓

Answer

Correct option: D.

$1.77 nC / m ^2$

(D) $1.77 nC / m ^2$
Explanation:

$\begin{array}{l} qE = mg \\ q
\left[\frac{\sigma}{2 \varepsilon_0}\right]= mg \end{array}$
$\sigma=\frac{2 \varepsilon_0 mg }{ q }$
$\sigma=\frac{2 \times 8.85 \times 10^{-12} \times 100 \times 10^{-6} \times 10}{10 \times 10^{-6}}$
$\sigma=17.7 \times 10^{-10} C / m ^2$
$\sigma=1.77 nC / m ^2$

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