Two isolated charged spheres each of magnitude + 1.0 x 10 ^ -6 C are seperated by a distance of 2.0 x 10 ^ -1…

Analyze the question: Two point-like charges are separated by a distance, and we need the force between them. This is a direct application of Coulomb's law.

Concept: Coulomb's law states that the force between two point charges is

F = k·q₁·q₂ / r²

where k = 9 × 10⁹ N m² C⁻², q₁ and q₂ are the charges, and r is the separation between them.

Solution:

Given:

• q₁ = q₂ = 1.0 × 10⁻⁶ C
• r = 2.0 × 10⁻¹ m = 0.2 m
• k = 9 × 10⁹ N m² C⁻²

Step 1: Multiply the charges. q₁q₂ = (1.0 × 10⁻⁶)(1.0 × 10⁻⁶) = 1.0 × 10⁻¹² C²

Step 2: Square the distance. r² = (0.2)² = 0.04 = 4.0 × 10⁻² m²

Step 3: Substitute into the formula. F = (9 × 10⁹)(1.0 × 10⁻¹²) / (4.0 × 10⁻²)

Numerator: 9 × 10⁹ × 10⁻¹² = 9 × 10⁻³

F = (9 × 10⁻³) / (4 × 10⁻²) = 2.25 × 10⁻¹ N

So F = 0.225 N, and since both charges are positive, the force is repulsive.

Answer: Option A, 2.25 × 10⁻¹ N.

Tip: In Coulomb's law questions, the most common mistake is forgetting to square the distance. Convert the distance to metres first, then square it. Also, powers of 10 are easy to handle if you combine them separately: 10⁹ × 10⁻¹² ÷ 10⁻² = 10⁻¹.