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Charged bob on a thread in a uniform field or near a charged sheet: angle, charge or tension at equilibrium

This type of question, asked 3 times: 1 Feb 2024, 2 Apr 2025, 22 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    1 Feb 2024

    120
    Suppose a uniformly charged wall provides a uniform electric field of 2×104 N/C2 \times10^{4}\text{ }N/C normally. A charged particle of mass 2 g2\text{ }g being suspended through a silk thread of length 20 cm20\text{ }cm and remain stayed at a distance of 10 cm10\text{ }cm from the wall. Then the charge on the particle will be 1xμC\frac{1}{\sqrt{x}}\mu C where x=x = ________ [use  g=10 m/s2]\left. \ g = 10\text{ }m/s^{2} \right\rbrack

  2. Question 2

    2 Apr 2025

    19
    A small bob of mass 100 mg and charge +10μC+ 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 ' σ\sigma ' as shown in figure. If string subtends an angle of 45∘45^{\circ} with the sheet at equilibrium the charge density of sheet will be : (Given, ε0=8.85×10−12 F m\varepsilon_{0}= 8.85 \times10^{- 12}\frac{\text{ }F}{\text{ }m} and acceleration due to gravity, g=10 m/s2g = 10\text{ }m/s^{2} )

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  3. Question 3

    22 Jan 2026 S1

    18
    A simple pendulum has a bob with mass mm and charge q . The pendulum string has negligible mass. When a uniform and horizontal electric field E→\overrightarrow{E} is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ____\_\_\_\_ . (g : acceleration due to gravity)

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