Answer:
F₃ = 590.625 N
Explanation:
We have a situation where, we have 3 Charges, as follows:
Charge 1 = q₁ = - 30 μC
Charge 2 = q₂ = 5 μC
Charge 3 = q₃ = 3 μC
Distance between Charge 3 and Charge 1 = r₃₁ = 4 cm = 0.04 m
Distance between Charge 3 and Charge 2 = r₃₂ = 4 cm = 0.04 m
So, in order to find net force on the charge 3:
F₃ = F₁₃ + F₂₃
where,
F₃ = Net force on charge 3
F₁₃ = Force on Charge 3 due to Charge 1
F₂₃ = Force on Charge 3 due to Charge 2
We are adding the magnitudes of forces, because their direction will be same. Since, charge 1 is negative and charge 3 is positive, so direction of force will be towards charge 1. And charge 2 is positive thus direction of its force will also be towards charge 1.
Now, using Coulomb Law:
F₃ = kq₁q₃/r₁₃² + kq₃q₂/r₁₂²
F₃ = kq₃ (q₁/r₁₃² + q₂/r₁₂²)
F₃ = (9 x 10⁹ N.m²/C²)(3 x 10⁻⁶ C)[(30 x 10⁻⁶ C)/(0.04 m)² + (5 x 10⁻⁶ C)/(0.04 m)²
F₃ = 590.625 N
