Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of -26e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of 46e), and then they are separated. The final charge on sphere W is 16e. What multiple of e gives the initial charge on sphere A?
Cannot be determined, unless you know something about the size of the spheres.
They're all the same size.
To find the multiple of e that gives the initial charge on sphere A, we need to examine the charges transferred during the touchings and separations.
Let's use the following notations:
- QW: The charge on sphere W
- QA: The charge on sphere A
- QB: The charge on sphere B
- QC: The charge on sphere C
Based on the given information:
1. Sphere W starts with an initial charge of zero, so QW = 0.
2. When sphere W is touched to sphere A and then separated, some charge is transferred from A to W.
3. When sphere W is then touched to sphere B and separated, some charge is transferred from B to W.
4. Finally, when sphere W is touched to sphere C and separated, some charge is transferred from C to W.
The final charge on sphere W is given as 16e, so QW = 16e.
Since sphere W starts with zero charge, the total charge on W after the first touching and separation (with sphere A) must be equal to the transferred charge from A to W.
Similarly, the total charge on W after the second touching and separation (with sphere B) must be equal to the transferred charge from B to W.
And the total charge on W after the third touching and separation (with sphere C) must be equal to the transferred charge from C to W.
Let's write down these relationships:
1. QW = QA (initial charge transferred from sphere A)
2. QW = QB (initial charge transferred from sphere B)
3. QW = QC (initial charge transferred from sphere C)
From these equations, we can conclude that QA = QB = QC = 16e.
Therefore, the multiple of e that gives the initial charge on sphere A (QA) is 16.