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An engineer measures a repulsive force of 5.5 mN between two identical ink drops, each carrying a charge of -1 x 10^-10 C. Using F = k q_inkdrop^2 / r^2, how far apart are the drops?
A5.5 x 10^-4 m
B1.3 x 10^-8 m
C1.3 x 10^-4 m
D1.3 x 10^-2 m
Answer & Solution
Correct answer: C. 1.3 x 10^-4 m
1. Convert the force to SI units: F = 5.5 mN = 5.5 x 10^-3 N.
2. Solve Coulomb's law for r: r = sqrt(k q^2 / F).
3. r = sqrt[(8.99 x 10^9 N m^2/C^2)(1 x 10^-10 C)^2 / (5.5 x 10^-3 N)] = sqrt(1.63 x 10^-8 m^2) = 1.3 x 10^-4 m.
4. Both drops carry the same sign of charge, so the force is repulsive, matching the given setup.
5. Option D misplaces a factor of 100 from a square-root slip, which is the usual trap when solving an inverse-square equation for distance.
_Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.2 Coulomb's law_
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