Twelve point charges are placed at the 1,2,3,…,12 positions of a circular clock dial. Starting from 1 o'clock and proceeding clockwise, the charges are -q, 2q, -3q, q, -q, 2q, -3q, q, -q, 2q, -3q, q. Each charge is at distance r from the centre. The electric field at the centre is:
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Question

Twelve point charges are placed at the 1,2,3,…,12 positions of a circular clock dial. Starting from 1 o'clock and proceeding clockwise, the charges are -q, 2q, -3q, q, -q, 2q, -3q, q, -q, 2q, -3q, q. Each charge is at distance r from the centre. The electric field at the centre is:

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G1 Physics · Accepted Answer

Diametrically opposite positions differ by six hours. In every opposite pair, the two charges are equal: q₁=q₇, q₂=q₈, …, q₆=q₁₂. Equal charges at diametrically opposite points produce equal and opposite electric fields at the centre. All six pairs cancel, so E n e t = 0. E_net=0. E n ​ e t = 0.