Question

in the diagram, q2 is +34.4*10^-6 C, and q3 is -72.8*10^-6 C. The net force on q2 is 225 N to the right. What is q1? Include the sign of the charge (+ or -). PLS HELP

Answer 1

Answer:

  q₁ = -6.54 10⁻⁵ C

Explanation:

Force is a vector quantity, but since all charges are on the x-axis, we can work in one dimension, let's apply Newton's second law

                F = F₁₂ + F₂₃

the electric force is given by Coulomb's law

                F = k q₁q₂ / r₁₂²

let's write the expression for each force

                F₂₃ = k q₂ q₃ / r₂₃²

                F₂₃ = 9 10⁹ 34.4 10⁻⁶ 72.8 10⁻⁶ / 0.1²

                F₂₃ = 2.25 10³ N

               

                F₁₂ = k q₁q₂ / r₁₂²

                F₁₂ = 9 10⁹ q₁ 34.4 10⁻⁶ / 0.1²

                F₁₂ = q₁   3,096 10⁷ N

we substitute in the first equation

                225 = q₁  3,096 10⁷ +2.25 10³

                q₁ = (225 - 2.25 10³) / 3,096 10⁷

                q₁ = -6.54 10⁻⁵ C