Final answer:
The correct ratio of Q: q that makes the total potential energy zero in the given system of charges is 2:1. This is derived by equating the potential energy between one -q and Q to the pair of -q charges, due to symmetry.
Step-by-step explanation:
The question pertains to the concept of electrical potential energy in a system of point charges within the field of Physics. The potential energy for any pair of charges is given by the formula (k * Q1 * Q2) / d, where k is Coulomb's constant, Q1 and Q2 are the magnitudes of the charges, and d is the distance between them. In this question, we have three charges -q, Q, and -q on a straight line at equal distances apart. We need to find the ratio Q: q that makes the total potential energy of this system equal to zero.
Given the symmetry of the arrangement, the potential energy contributions from the pairs -q and Q, and Q and -q must be equal and opposite to cancel out the potential energy contribution from the pair of -q charges, making the total potential energy zero. Therefore, without the loss of generality, we can equate the potential energy between one -q and Q to the potential energy between the two -q charges. From this, we can derive that Q = 2q, and thus the correct answer to the ratio of Q: q is 2:1.