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

q₁ = -6.54 10⁻⁵ C

Step-by-step 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