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Field at the centre of a uniformly charged arc or half ring

This type of question, asked 3 times: 2021 Paper 21, 4 Apr 2025, 6 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 21

    20
    Figure shows a rodABrodAB, which is bent in a 120∘120^{\circ} circular arc of radius R. A charge (−Q)( -Q) is uniformly distributed over rod ABAB. What is the electric field E→\overrightarrow{E} at the centre of curvature OO?

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  2. Question 2

    4 Apr 2025

    82
    A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

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  3. Question 3

    6 Apr 2026 S1

    13
    A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at center of the half ring is 100 V/m100\text{ }V/m, then the value of Q is ____\_\_\_\_ nC. ( ϵ0=8.85×10−12C2/Nm2\epsilon_{0}= 8.85 \times10^{- 12}C^{2}/Nm^{2} and π=3.14\pi= 3.14 )

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