Two identical charges q₁ = q₂ = 5 μC. Find largest charge q to transfer so force decreases to 1/2.5 of original.

Step-1: After transferring charge q: new charges = (5−q) and (5+q) μC

Step-2: New force = F₀ / 2.5:

k(5−q)(5+q)/r² = k×25/(2.5×r²) = 10k/r²

(5−q)(5+q) = 10

25 − q² = 10 ⇒ q² = 15 ⇒ q = √15 μC

Answer: q = √15 μC ≈ 3.87 μC

Note: (5−q)(5+q) = 25−q² is the difference-of-squares identity. Transferring charge always decreases the product q₁q₂ for charges of the same sign.