A force of 85 N acts between two charges 3.2 cm apart. One charge has magnitude 25 μC. Find the other charge magnitude.

Solution & explanation

1. Given: F = 85 N; r = 3.2 cm; q₁ = 25 μC; k = 9×10⁹.

2. Convert separation to metres.

   $$r=\frac{3.2}{100}=0.032$$

3. Convert charge to coulombs.

   $$q_1=\frac{25}{1000000}$$

4. Rearrange Coulomb’s magnitude equation.

   $$q_2=\frac{F\times r^2}{k\times q_1}$$

5. Substitute SI values.

   $$q_2=\frac{0.08704}{\frac{225000000000}{1000000}}$$

6. Compute numerator and denominator separately.

   $$q_2=\frac{0.08704}{225000}$$

7. Divide, then convert C to μC.

   $$q_2=3.86844444444444·{10}^{-7}$$

8. State the result with units: q₂ ≈ 0.387 μC. Force magnitude alone does not give its sign.

q₂ ≈ 0.387 μC