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Charges Q each are placed on four corners of a regular pentagon. The distance of each corner from the centre of the pentagon is r. The electric field at its centre is

Asked in GSEB Board July 2018 · Field of discrete charges

• (1) (KQ)/(r²)
• (2) (5KQ)/(4r²)
• (3) (4KQ)/(r²)
• (4) (4KQ)/(5r²)

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives (5KQ)/(4r²). Sanity check: the four fields, spaced 72° apart, add up to exactly the field one corner charge would make, (KQ)/(r²).
• (3) Adds the four magnitudes as if all four fields pointed the same way. They point away from four different corners, and most of their components cancel.
• (4) No single slip gives (4KQ)/(5r²). Sanity check: five equal charges give zero at the centre, so four give the field of the missing one, (KQ)/(r²).

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