Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -8q. Sphere B carries a charge of +7q. 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) 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?
(c) What is the total charge on the three spheres after they have touched?
Facts
proton mass = 1.673x10^-27 kg
neutron mass = 1.675x10^-27kg
electron mass = 9.11x^10^-31kg
e= 1.60x10^-19C
q=Ne
q respresents electrical charge
How do I put all of this infomation together to answer this question. Am I over thinking this problem. Please help!
To answer these questions, we need to consider the principles of electrical charge and conservation of charge.
(a) How much charge ends up on sphere C?
When spheres A and B are touched together and then separated, they will share their charges equally since they are identical. So, sphere A will have a charge of -7q and sphere B will have a charge of +7q.
When sphere C is touched to sphere A and separated, they will also share their charges equally. So, sphere C will have a charge of -7q.
When sphere C is touched to sphere B and separated, they will again share their charges equally. So, sphere C will have a charge of -7q.
Therefore, the charge on sphere C ends up being -7q.
(b) What is the total charge on the three spheres before they are allowed to touch each other?
Before they touch each other, sphere A has a charge of -8q, sphere B has a charge of +7q, and sphere C has no net charge. So, the total charge is (-8q + 7q + 0) = -q.
(c) What is the total charge on the three spheres after they have touched?
After they have touched, sphere A has a charge of -7q, sphere B has a charge of +7q, and sphere C has a charge of -7q. So, the total charge is (-7q + 7q - 7q) = -7q - 7q = -14q.
Therefore, the total charge on the three spheres after they have touched is -14q.
To answer these questions, you will need to apply the principle of conservation of charge. According to this principle, charge is neither created nor destroyed; it is only transferred from one object to another.
(a) To determine the charge on sphere C after the described process, you need to consider the individual charges acquired through each step.
1. When sphere A (-8q) and sphere B (+7q) are touched together and then separated, charge is transferred between them until they reach the same potential. Since the spheres are identical, they will share the charge equally. Therefore, each sphere will have a charge of -0.5q and +0.5q, respectively. The transfer of charge ensures that the total charge remains the same.
2. When sphere C is touched to sphere A (-0.5q) and separated, sphere C acquires an equal but opposite charge. Therefore, sphere C will have a charge of +0.5q.
3. When sphere C is touched to sphere B (+0.5q) and separated, sphere C acquires an equal charge, which is +0.5q.
Therefore, the charge on sphere C at the end of the process is +0.5q.
(b) Before the spheres are allowed to touch each other, the total charge on the three spheres can be calculated by summing the individual charges on each sphere.
Sphere A: -8q
Sphere B: +7q
Sphere C: 0q
Hence, the total charge on the three spheres before they touch is -8q + 7q + 0q = -q.
(c) After the spheres have touched each other and the charge has been redistributed, the total charge on the three spheres remains the same as before, since charge is conserved. Therefore, the total charge on the three spheres after they have touched is also -q.
In summary:
(a) The charge on sphere C is +0.5q.
(b) The total charge on the three spheres before touching is -q.
(c) The total charge on the three spheres after touching remains -q.
Remember, to solve problems like this, it is essential to apply the principles of conservation and carefully consider the transfer of charges during each step.