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 touched to sphere a and separated from it. last, sphere c is touched to sphere b and separated from it. a) how much charge ends up on sphere c? b) what is the total charge on the three spheres before they are allowed to touch each other and c) after they have touched?
Let's break down the steps and go through each one:
a) When spheres A and B are touched together and then separated, the charges redistribute. The final charges on spheres A and B can be found by considering charge conservation.
Initially, Sphere A has a charge of +5q, and Sphere B has a charge of -q.
When touched together, electrons will flow from Sphere A to Sphere B until the charges are equalized due to their conductive nature.
Since the spheres are identical, the charges will share equally. So, each sphere will have a charge of (5q - q)/2 = 2q.
When Sphere C is touched to Sphere A and then separated, the charges will redistribute again. However, Sphere C has no net charge initially.
Since Sphere A had a charge of 2q, the contact will induce redistribution of charge, leaving a final charge of q on Sphere A and q on Sphere C.
When Sphere C is touched to Sphere B and separated, Sphere B has a charge of -q and Sphere C has a charge of q.
Again, the charges will redistribute, and electrons will flow until the charges are equalized.
Since the spheres are identical, the charges will again share equally. So, each sphere will have a final charge of (-q + q)/2 = 0.
Therefore, sphere C ends up with a charge of 0.
b) Before the spheres are allowed to touch, the total charge on the three spheres is the combined charge of A, B, and C, which is:
+5q + (-q) + 0 = 4q.
c) After the spheres have touched, the charges redistribute as explained above. So, the total charge on the three spheres is the combined charge of A, B, and C, which is:
+q + q + 0 = 2q.
To answer these questions, we need to understand the concept of charge conservation and the transfer of charge through the process of touching and separation. Let's break it down step by step:
a) How much charge ends up on sphere c?
When sphere a and b are touched together and separated, charge is transferred from one sphere to another. Since sphere a carries a charge of +5q and sphere b carries a charge of -q, the total charge transferred is +5q - q = +4q. This means that after touching and separation, sphere a gains a charge of +4q and sphere b loses a charge of -q. Now, when sphere c is touched to sphere a and separated, the charge is transferred again. Sphere c will acquire the same charge as sphere a, so the charge on sphere c will be +4q.
b) What is the total charge on the three spheres before they are allowed to touch each other?
Initially, before any touching occurs, sphere a carries a charge of +5q, sphere b carries a charge of -q, and sphere c carries no net charge. So the total charge on the three spheres is +5q + (-q) + 0 = +4q.
c) What is the total charge on the three spheres after they have touched?
After the whole process of touching and separation, the charge on sphere a becomes +4q, the charge on sphere b becomes 0 (as it loses all its charge), and the charge on sphere c becomes +4q (acquired from sphere a). So the total charge on the three spheres is +4q + 0 + +4q = +8q.
In summary:
a) The charge on sphere c ends up being +4q.
b) The total charge on the three spheres before they touch is +4q.
c) The total charge on the three spheres after they touch is +8q.