A -9.00 μC point charge and +7.00 μC point charge are placed along the x-axis at x = 0.000 m and x = 0.4 m, respectively. Where must a third charge be placed along the x-axis (relative to the origin) so that it does not experience any net electric force due to the other two charges? The position on the x-axis is in meters and use three significant digits.

x₃ = 0.397 m

Explanation:

For this exercise we use the vector sum of the forces, where the force is electric given by the Coulomb equation

           F =

We also use that charges of the same sign repel and charges of a different sign attract.

   In this case the force between load 1 and 3 has one direction and the force between 2 and 3 has the opposite direction, in the exercise they ask that the force on load 3 be zero

           ∑ F = F₁₃ - F₂₃ = 0

            F₁₃ = F₂₃

we write the expressions of the forces, the distances are

         r₁₃ = (x₁-x₃) ²

         r₂₃ = (x₂ - x₃) ²

x₁ = 0 m

         q₁ (x₂ - x₃) ² = q₂ x₃²

          (x₂ -x₃) = x₃

we substitute the values

           (0.4 -x₃) = x₃

         x₃ (1 + ) =  0.4

         x₃ (1.13389) = 0.453557

         x₃ = 0.453557 / 1.13389

         x₃ = 0.397 m

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

thermal energy is the answer