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JEE Main 20241 FebruaryEvening Shift
Exam
JEE Main
Year
2024
Date
1 February
Shift
Evening Shift
Subject
Physics
Chapter
Electrostatics

JEE Main 2024 · 1 February · Evening Shift · Physics · Electrostatics

Suppose a uniformly charged wall provides a uniform electric field...

Suppose a uniformly charged wall provides a uniform electric field of 2×104NC−12 \times {10}^{4}N{C}^{- 1} normally. A charged particle of mass 2g2g being suspended through a silk thread of length 20cm20cm and remain stayed at a distance of 10cm10cm from the wall. Then the charge on the particle will be 1x\muC\dfrac{1}{\sqrt{x}}\muC where x=x = ________ [use g=10ms−2g = 10m{s}^{- 2}]Suppose a uniformly charged wall provides a uniform electric field of 2 × 10 ^ 4 N C ^ - 1 normally. A charged particle

Correct answer

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Step-by-step solution

Suppose a uniformly charged wall provides a uniform electric field of 2 × 10 ^ 4 N C ^ - 1 normally. A charged particle

As we can see from geometry, sinθ=1020=12sin\theta = \dfrac{10}{20} = \dfrac{1}{2}

⇒θ=30°⇒ \theta = 30 °

Vertical component of tension will balance the weight and the horizontal component will balance the electric force. Therefore,

tanθ=qEmgtan\theta = \dfrac{qE}{mg}

⇒tan⁡30°=q×2×1042×10−3×10⇒ \tan 30 ° = \dfrac{q \times 2 \times {10}^{4}}{2 \times {10}^{- 3} \times 10}

⇒13=q×106⇒ \dfrac{1}{\sqrt{3}} = q \times {10}^{6}

⇒q=13×10−6C=13μC⇒ q = \dfrac{1}{\sqrt{3}} \times {10}^{- 6}C = \dfrac{1}{\sqrt{3}}\mu C

Hence, x=3x = 3.

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