(Solved): (13\%) Problem 6: Three charged particles lie in the \( x y \) plane at an angle of \( \theta \) re ...

(13\%) Problem 6: Three charged particles lie in the \( x y \) plane at an angle of \( \theta \) relative to the \( x \) axis. Charge \( q_{1} \) is located at the origin, \( q_{2} \) is a distance \( r \) from \( q_{1} \), and \( q_{3} \) is a distance \( 3 r \) from \( q_{1} \). The charges each have magnitude of \( q \), but \( q_{1}=q_{2}=+q \), and \( q_{3}=-q \). Charges \( q_{1} \) and \( q_{3} \) are fixed, and \( q_{2} \) can move. However, \( q_{1} \) and \( q_{2} \) are connected by an ideal, neutral spring of spring constant \( k_{\mathrm{s}} \). The spring is initially not stretched. Let Coulomb's constant be \( k_{\mathrm{e}} \cdot q_{1} \) and \( q_{2} \) are positive and \( q_{3} \) is negative. \$ 25\% Part (a) Choose the best expression for the net electrostatic force on \( q_{2} \) in terms of the given variables.