Step-by-step explanation:
To calculate the net force on particle q₂, we need to consider the forces exerted on it by the other two particles. The force between two charged particles can be calculated using Coulomb's law:
F = k * (|q₁| * |q₂|) / r²
Where: F is the force between the particles. k is Coulomb's constant, approximately equal to 8.99 × 10^9 N m²/C². |q₁| and |q₂| are the magnitudes of the charges of the particles. r is the separation distance between the particles.
Let's calculate the forces between q₁ and q₂, and between q₂ and q₃:
Force between q₁ and q₂: F₁₂ = k * (|q₁| * |q₂|) / r₁₂²
Given: q₁ = +18.1 μC (microcoulombs) q₂ = -11.2 μC (microcoulombs) r₁₂ = 0.280 m
Calculating the magnitude of F₁₂:
|F₁₂| = (8.99 × 10^9 N m²/C²) * ((18.1 × 10^-6 C) * (11.2 × 10^-6 C)) / (0.280 m)²
|F₁₂| ≈ 1.839 N
The force between q₁ and q₂ is approximately 1.839 N, and since q₁ is positive and q₂ is negative, the force will point to the left (-F₁₂).
Force between q₂ and q₃: F₂₃ = k * (|q₂| * |q₃|) / r₂₃²
Given: q₂ = -11.2 μC (microcoulombs) q₃ = +5.67 μC (microcoulombs) r₂₃ = 0.350 m
Calculating the magnitude of F₂₃:
|F₂₃| = (8.99 × 10^9 N m²/C²) * ((11.2 × 10^-6 C) * (5.67 × 10^-6 C)) / (0.350 m)²
|F₂₃| ≈ 0.512 N
The force between q₂ and q₃ is approximately 0.512 N, and since both q₂ and q₃ are positive, the force will point to the right (+F₂₃).
To calculate the net force on q₂, we need to consider the vector sum of the forces:
Net force = F₁₂ + F₂₃
Net force ≈ -1.839 N + 0.512 N
Net force ≈ -1.327 N
Therefore, the net force on particle q₂ is approximately -1.327 N, pointing to the left.