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Consider three identical metal spheres, a, b, and

c. sphere a carries a charge of +5q. sphere b carries a charge of -q. sphere c carries no net charge. spheres a and b are touched together and then separated. sphere c is then touched to sphere a and separated from it. lastly, sphere c is touched to sphere b and separated from it. (a) what is the ratio of the final charge on sphere c to q? what is the ratio of the final total charge on the three spheres to q (b) before they are allowed to touch each other and (c) after they have touched?

User Khanna
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Final answer:

The final charge on sphere c is equal to q, so the ratio of the final charge on sphere c to q is 1:1. The total charge on all three spheres remains as +4q both before and after they have touched, resulting in a ratio of 4:1.

Step-by-step explanation:

When dealing with the conduction of charge between identical conducting spheres, the total charge is distributed evenly among them once the spheres are brought into contact and separated. In the given scenario with three identical metal spheres, a, b, and c, where sphere a carries a charge of +5q, sphere b carries a charge of -q, and sphere c is initially uncharged, the following will occur:

  • When sphere a (+5q) is touched to sphere b (-q), they will share the total charge of +4q equally, each sphere ending up with +2q after separation.
  • Touching sphere c (0q) to sphere a (+2q) then results in a distribution of +2q between two spheres, so both will carry +1q after separation.
  • Finally, touching sphere c (+1q) to sphere b (+2q) makes three identical spheres with a total charge of +3q. This total charge will be distributed evenly, so each sphere will carry +1q after separation.

Thus, the ratio of the final charge on sphere c to q is 1:1. The final total charge on the three spheres before touching each other was +5q - q +0q = +4q, and after touching, it remains the same, thus the ratio remains 4:1.

User Vii
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Due to the conservation of charge, the total number of charges remain constant. The initial charge is +5q+(-1)q+0=4q, so the system end up with 4q. When sphere a and b touch, their charge become equal, so each takes on a charge of (+5-1)/2=2q. The a and c touch each other and evenly divide the total charge, each takes on a charge of 2/2=1q. Lastly, b and c touch each other, each has (2+1)/2=1.5q.
User Colin Armstrong
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