This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Define the positions of the charges. Let the charge q_1 = q be placed at the origin, x_1 = 0. Let the charge q_2 = -3q be placed at x_2 = d. Let the third charge q_3 = 2q be placed at an unknown position x. Step 2: Determine the region for zero net force. For the net force on q_3 to be zero, the forces due to q_1 and q_2 must be equal in magnitude and opposite in direction. Since q_1 and q_2 have opposite signs (q is positive, -3q is negative), the equilibrium point cannot be between them. If q_3 (positive) is between q_1 and q_2, q_1 would repel it to the right, and q_2 would attract it to the right. Both forces would be in the same direction, so they cannot cancel. Therefore, the equilibrium point must be outside the region 0 < x < d. Also, for the forces to cancel, the third charge must be closer to the charge with the smaller magnitude. Here, |q_1| = |q| and |q_2| = |-3q| = 3|q|. Since $|