Final answer:
The maximum force of repulsion between charges Q1 and Q2, derived from a total charge Q and placed at a distance R from each other, occurs when Q1 = Q/2 and Q2 = Q/2.
Step-by-step explanation:
The question pertains to the interaction of electric charges and seeks to determine when the force of repulsion is at its maximum between two charges Q1 and Q2 derived from a parent charge Q and situated at a distance R from each other. According to Coulomb's law, the force between two charges is proportional to the magnitude of each charge and inversely proportional to the square of the distance between them. This interaction is repulsive when the charges carry the same type of electric charge.
Calculating the maximization of this force with respect to the distribution of charge Q into Q1 and Q2, you will find that the force is at its maximum when Q1 and Q2 are equal, meaning when Q1 = Q/2 and Q2 = Q/2. This ensures that the product of the magnitudes of the two charges (which directly influences the force) is maximized as well.
The option that states Q1 = Q/2 and Q2 = Q/2 is therefore the correct distribution of charges to maximize the repulsive force.
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