Answer:
E) Either (B) or (D) will work
Step-by-step explanation:
In the first case with source positive charge Qs and q₀
the electric force is: K = 9 * 10⁹ Nm²C⁻²
Fe₁ = K * Qs*q₀ / r₁² (1)
In the second case with source positive charge 2Qs and q₀
the electric force is:
Fe₂ = K * 2*Qs*q₀ / r₂²
If the forces Fe₁ and Fe₂ are to be equal then:
Fe₁ = Fe₂
K * Qs*q₀ / r₁² = K * 2*Qs*q₀ / r₂²
1/r₁² = 2/r₂² or r₂² = 2* r₁²
r₂ = √ 2 * r₁
Then if we want to keep the same force we need to increase r₂ by a factor √2.
If we have q₀₂ = 1/2 * q₀
Fe₃ = K * 2*Qs* (1/2)*q₀ / r₁²
we can see that Fe₃ = K* Qs*q₀ / r₁² , and this expression is the same that Fe₁ = K * Qs*q₀ / r₁² .
Again we can have the same electric force if we halve the charge q₀/2
