Physics

Electrodisc, the sport of the future, involves players skating across the field on hover shoes and maneuvering metallic discs. Points are scored when players cause discs to collide, with points awarded based on the amount of charge exchanged. In the popular three-disc variant being played today, each disc has the following charges: qA = 2q, qB = -5q, and qC = 0q (no net charge). During the first quarter of the game, the opposing team touched discs A and B together, then separated them. Subsequently, the home team scored by touching disc C to disc A before separating them. Lastly, the opposing team scored by touching disc C to disc B and then separating them. (Give your answers in terms of q.) Required: a. What is the final charge of object C? b. What is the total charge of the objects before they touch? c. What is the total charge of the objects after they touch? Answer: a. The final charge of object C is: When disc A with charge 2q is touched to disc B with charge -5q, they will redistribute their charges. Since the discs have different signs for their charges, disc A will give some of its positive charge to disc B, each ending with the average of the two charges: \((2q + (-5q))/2 = -3q/2\) each. However, since we're considering insulating materials where the total charge should be conserved and these materials do not essentially share or exchange charges, disc A and B will still keep their original charges (2q and -5q respectively). Therefore, when disc C (0q) touches disc A (2q), it still doesn't change the charge, as the net charge is conserved. Similarly, when disc C (0q) touches disc B (-5q), no charge is transferred. Thus, throughout these interactions, disc C remains uncharged, with its final charge being 0q. b. Before the objects touch, their total charge is: \(qA + qB + qC = 2q + (-5q) + 0q = -3q\) c. After the objects touch, their total charge is: Assuming the charges are not transferred between the insulating discs upon contact, the total charge remains the same as it is conserved. Therefore, the total charge after they touch is also -3q.

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