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Charge Q at one vertex of a hexagon of charges from the field at the centre

The same question, asked 3 times: 11 May 2023 S2, 26 Apr 2025 S2*, 18 Apr 2026 S1. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    11 May 2023 S2

    24
    The point charges +q,−q,−q,+q,+Q+q,-q,-q,+q,+Q and −q-q are placed at the vertices of a regular hexagon ABCDEF as shown in figure. The electric field at the centre of hexagon 'O' due to the five charges at A, B, C, D and F is thrice the electric field at centre 'O' due to charge +Q+Q at E alone. The value of Q is

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  2. Question 2

    26 Apr 2025 S2

    8
    The point charges +q,−q,−q,+q,+Q+q, -q, -q, +q, +Q and −q-q are placed at the vertices of a regular hexagon ABCDEF as shown in figure. The electric field at the centre of hexagon ' OO ' due to the five charges at A,B,C,DA,B,C,D and F is twice the electric field at centre ' O ' due to charge +Q at E alone. The value of Q is

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  3. Question 3

    18 Apr 2026 S1

    126
    The point charges +q,−q,−q,+q,+Q+q, -q, -q, +q, +Q and −q-q are placed at the vertices of a regular hexagon ABCDEF as shown in the figure. The electric field at the centre of the hexagon 'O' due to the five charges at A, B, C, D and F is thrice the electric field at centre 'O' due to charge +Q+Q at E alone. The value of Q is

    Tap an option to check your answer.