Question Detail
Question
Three point charges lie along the x-axis. The positive charge q1 = 15.0 uC is at x = 2.00 m, the positive charge q2 = 6.00 uC is at the origin, and the resultant force on q3 (negative) is zero. What is the x-coordinate of q3?
Correct Answer
Option A is the correct answer.
Detailed Explanation
Let q3 be at position x (0<x<2), pulled toward both q1 and q2 (opposite signs attract), so equilibrium means the two attractive forces balance: k q2 q3/x2 = k q1 q3/(2-x)2 6/x2 = 15/(2-x)2 6(2-x)2 = 15x2 (2-x)2 = 2.5x2 2 - x = sqrt(2.5) x = 1.581x 2 = 2.581x => x = 0.775 m.
Hint
Let q3 be at position x (0