Calculate the potential at the centre of a square ABCD of each side...

Question

Calculate the potential at the centre of a square ABCD of each side √2 m due to charges 2, −2, −3 and 6 µC at the four corners.

Accepted Answer

Given:
• Side of square = √2 m
• Charges: q₁ = 2 µC, q₂ = −2 µC, q₃ = −3 µC, q₄ = 6 µC

Step 1 — Distance from Corner to Centre:
Diagonal of square = √2 × side = √2 × √2 = 2 m
r = diagonal / 2 = 2/2 = 1 m

Step 2 — Net Charge:
ΣQ = (2 − 2 − 3 + 6) µC = 3 µC = 3 × 10⁻⁶ C

Step 3 — Potential at Centre:
V = k × ΣQ / r
= (9 × 10⁹ × 3 × 10⁻⁶) / 1
= 2.7 × 10⁴ V

∴ Potential at centre = 27,000 V = 2.7 × 10⁴ V

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