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Point on the line of two charges where the field (or the force on a third charge) is zero

This type of question, asked 5 times: 2021 Paper 22, 25 Jan 2023, 29 Jan 2023, 31 Jan 2024, 2 Apr 2025. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 22

    3
    Two particles AA and BB having charges 20μC20\mu C and −5μC- 5\mu C respectively are held fixed with a separation of 5 cm5\text{ }cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

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  2. Question 2

    25 Jan 2023

    108
    A point charge of 10μC10\mu C is placed at the origin. At what location on the XX-axis should a point charge of 40μC40\mu C be placed so that the net electric field is zero at x=2 cmx = 2\text{ }cm on the X-axis?

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  3. Question 3

    29 Jan 2023

    29
    A point charge q1=4q0q_{1}= 4q_{0} is placed at origin. Another point charge q2=−q0q_{2}= -q_{0} is placed at x=12 cmx = 12\text{ }cm. Charge of proton is q0q_{0}. The proton is placed on xx axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is___ cmcm.
  4. Question 4

    31 Jan 2024

    12
    Two charges qq and 3q3q are separated by a distance ' rr ' in air. At a distance xx from charge qq, the resultant electric field is zero. The value of xx is:

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  5. Question 5

    2 Apr 2025

    7
    A point charge +q is placed at the origin. A second point charge +9 q is placed at (d,0,0)(d,0,0) in Cartesian coordinate system. The point in between them where the electric field vanishes is :

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