Two small equally charged metal spheres each have charge 3 μC and are 2.0 cm apart. Calculate their repulsive force.

Solution & explanation

1. Given: q₁ = q₂ = 3 μC; r = 2.0 cm; k = 9×10⁹.

2. Convert charge and distance to SI.

   $$q=\frac{3}{1000000}$$

3. Convert 2 cm to 0.02 m.

   $$r=\frac{2}{100}=0.02$$

4. Equal charges give F = kq²/r².

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

5. Insert the values.

   $$F=\frac{\frac{81}{1000}}{{0.02}^2}$$

6. Square charge and separation separately.

   $$F=\frac{0.081}{0.0004}=202.5$$

7. State the result with units: F = 202.5 N on each sphere, in opposite directions.

F = 202.5 N