Three charged particles lie in the xy plane at an angle of relative to the x -axis. Charge q 1 is located at the

Three charged particles lie in the xy plane at an angle of θ relative to the x-axis. Charge q₁ is located at the origin, q₂ is a distance r from q₁, and q₃ is a distance 3r from q₁. The charges each have magnitude of q, but q₁ = q₂ = +q, and q₃ = -q. Charges q₁ and q₃ are fixed, and q₂ can move. However, q₁ and q₂ are connected by an ideal, neutral spring of spring constant k_s. The spring is initially not stretched. Let Coulomb’s constant be k_e. q₁ and q₂ are positive and q₃ is negative.

Write the best expression for the net electrostatic force on q₂, in terms of the given variables.

Part (b)Because the force on q₂ is nonzero, it will begin to move from rest. In which direction will it move?
Part (c)When q₂ begins to move, it will stretch the spring. Choose the equation for the force vector from the spring, F_s, due to stretching the spring a distance of Δr.
Part (d)When q₂ is at its equilibrium position, the forces acting on it will be balanced. Which of the expressions below correctly shows the electrostatic force on q₂ when the charge has reached its equilibrium position?
 

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