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 \(\frac{1}{\sqrt{\mathrm{x}}} \ \mu \mathrm{C}\) where \(\mathrm{x}=\) _______ [use \(g=10 \mathrm{~m} / \mathrm{s}^2\)]

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Verified Solution

Answer & Solution

Correct Answer

(B) \(3\)

Detailed explanation

\(\sin \theta=\frac{10}{20}=\frac{1}{2}\)

\(\theta=30^{\circ}\)

\(\tan \theta=\frac{\mathrm{qE}}{\mathrm{mg}}\)

\(\tan 30^{\circ}=\frac{\mathrm{q} \times 2 \times 10^4}{1 \times 10^{-3} \times 10}\)

\(\frac{1}{\sqrt{3}}=\mathrm{q} \times 10^6\)

\(\mathrm{q}=\frac{1}{\sqrt{3}} \times 10^{-6} \mathrm{C}\)

\(x=3\)

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