Two equally charged spheres repel with 0.5 N at separation 3 cm in air. Find the magnitude of charge on each.

Solution & explanation

1. Given: F = 0.5 N; r = 3 cm = 0.03 m; k = 9×10⁹.

2. Start with equal-charge Coulomb force.

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

3. Multiply by r² and divide by k.

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

4. Substitute.

   $$q^2=\frac{0.00045}{9\times {10}^9}$$

5. Square 0.03, multiply by 0.5, then divide.

   $$q^2=\frac{0.00045}{9\times {10}^9}=\frac{5}{100000000000000}$$

6. Take the positive square root because a magnitude is requested.

   $$q=\sqrt{\frac{5}{100000000000000}}$$

7. The value is about 2.236×10⁻⁷ C; multiply by 10⁶ for μC.

8. State the result with units: q ≈ 0.224 μC = 224 nC per sphere.

q ≈ 0.224 μC = 224 nC