The answer is A. 1/4 as much.
To calculate this, we will use Coulomb's Law:
F = kQ1Q2/r²
where F is repulsive force, k is constant, Q is charge, r is distance between charges.
k = 5.0 × 10⁹ Nm/C²
Let's take one example where:
Q1 = Q2 = 1.2 × 10⁻⁶ C²
r₁ = 0.5 m
So, F1 = kQ1Q2/r₁² = 5.0 × 10⁹ 1.2 × 10⁻⁶ 1.2 × 10⁻⁶ /0.5² = 12.96 × 10⁻²/0.25 = 51.84 × 10⁻² = 0.5184 ≈ 0.52
Let's now double r:
r₂ = 2r₁ = 20.5 = 1
And let's calculate force:
F2 = kQ1Q2/r₂² = 5.0 × 10⁹ 1.2 × 10⁻⁶ 1.2 × 10⁻⁶ /1² = 12.96 × 10⁻²/1 = 12.96 × 10⁻² = 0.1296 ≈ 0.13
And now, let's see how much is the second force (F2) differ from the first force (F1):
F2/F1 = 0.13/0.52 = 1/4
