Spheres A, B, and C have charges +8.0 C, +12.0 C, and -5.0 C, respectively. The three spheres are allowed to touch each other
To determine the final charges on the spheres after they touch each other, we first need to understand the concept of charge transfer.
When two charged objects come into contact, electrons can be transferred from one object to another. The number of electrons transferred depends on the difference in charge between the objects. Electrons will move from the object with a higher negative charge (excess of electrons) to the object with a lower negative (or positive) charge.
In this case, let's consider the initial charges of the spheres:
Sphere A: +8.0 C
Sphere B: +12.0 C
Sphere C: -5.0 C
Step 1: Determine the charge transferred between Sphere A and Sphere C:
Since Sphere A has a positive charge and Sphere C has a negative charge, electrons will be transferred from Sphere A to Sphere C. The magnitude of the charge transferred will depend on the difference in charges. In this case, the difference is 8.0 C - (-5.0 C) = 13.0 C.
Step 2: Determine the new charges after the charge transfer:
The charge transferred will be evenly divided between the two spheres.
Sphere A will lose half of the transferred charge, which is 6.5 C. Therefore, its new charge will be 8.0 C - 6.5 C = +1.5 C.
Sphere C will gain half of the transferred charge, which is also 6.5 C. Therefore, its new charge will be -5.0 C + 6.5 C = +1.5 C.
Step 3: Determine the charge transferred between Sphere B and the combined charge of A and C:
Since Sphere B has a larger positive charge than the combined charge of A (+1.5 C) and C (+1.5 C), electrons will be transferred from Sphere B to the combined charge of A and C. The difference in charge is 12.0 C - (1.5 C + 1.5 C) = 12.0 C - 3.0 C = 9.0 C.
Step 4: Determine the final charges after the second charge transfer:
The charge transferred will be evenly divided between the two spheres (A and C).
Each sphere (A and C) will gain half of the transferred charge, which is 4.5 C.
Therefore, Sphere A's new charge will be 1.5 C + 4.5 C = +6.0 C.
Similarly, Sphere C's new charge will be 1.5 C + 4.5 C = +6.0 C.
Thus, after the spheres touch each other, the final charges are:
Sphere A: +6.0 C
Sphere B: -5.0 C
Sphere C: +6.0 C