Electrostatics Question 3
Question 3 - 2024 (01 Feb Shift 2)
Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^{4} \mathrm{~N} / \mathrm{C}$ normally. A charged particle of mass $2 \mathrm{~g}$ being suspended through a silk thread of length $20 \mathrm{~cm}$ and remain stayed at a distance of $10 \mathrm{~cm}$ from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{x}} \mu \mathrm{C}$ where $\mathrm{x}=$ [use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ ]
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Answer: (3)
$\sin \theta=\frac{10}{20}=\frac{1}{2}$
$\theta=30^{\circ}$
$\tan \theta=\frac{\mathrm{qE}}{\mathrm{mg}}$
$\tan 30^{\circ}=\frac{q \times 2 \times 10^{4}}{1 \times 10^{-3} \times 10}$
$\frac{1}{\sqrt{3}}=\mathrm{q} \times 10^{6}$
$\mathrm{q}=\frac{1}{\sqrt{3}} \times 10^{-6} \mathrm{C}$
$\mathrm{x}=3$
