Two equal and similar charges 3 cm apart in air repel each other with a force of 1.6 N. What will be the magnitude of each charge?

$4 × 10^{-7} C$

The correct answer is Option (3) → $4 × 10^{-7} C$

Given: Two equal charges $q$ separated by $r = 0.03 \, \text{m}$ repel each other with a force $F = 1.6 \, \text{N}$. Permittivity of free space: $\epsilon_0 = 8.854 \times 10^{-12} \, \text{F/m}$.

Coulomb's law: $F = \frac{1}{4 \pi \epsilon_0} \frac{q^2}{r^2} \;\Rightarrow\; q = \sqrt{F \cdot 4 \pi \epsilon_0 \cdot r^2}$

$4 \pi \epsilon_0 = 4 \pi \cdot 8.854 \times 10^{-12} \approx 1.112 \times 10^{-10}$

$F \cdot 4 \pi \epsilon_0 \cdot r^2 = 1.6 \cdot 1.112 \times 10^{-10} \cdot (0.03)^2 \approx 1.6 \times 10^{-13}$

$q = \sqrt{1.6 \times 10^{-13}} \approx 4 \times 10^{-7} \, \text{C}$

Magnitude of each charge ≈ 4 × 10⁻⁷ C