Five equal positive charges occupy five vertices of a regular hexagon. The electric field at the centre is E₁. A negative charge of the same magnitude is placed at the sixth vertex and the new field is E₂. Find E₂/E₁.
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Question

Five equal positive charges occupy five vertices of a regular hexagon. The electric field at the centre is E₁. A negative charge of the same magnitude is placed at the sixth vertex and the new field is E₂. Find E₂/E₁.

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G1 Physics · Accepted Answer

Step 1: The field of six equal positive charges at the centre of a regular hexagon is zero. Therefore the field E₁ due to five positive charges is equal and opposite to the field that the missing sixth positive charge would produce. Step 2: Replacing the missing +q by −q reverses that single-charge field, so it adds in the same direction as E₁. Hence E₂=2E₁ and E₂/E₁=2. Final: A.