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? (All 4 spheres are the same size)
To solve this problem, we need to understand the concept of charge conservation. According to the principle of charge conservation, the total charge before and after any interaction remains constant.
Let's analyze each interaction step by step:
1. Sphere W is touched to sphere A (initial charge of zero): When two objects touch each other, charge is transferred between them until they reach equilibrium. In this case, sphere W gains some charge from sphere A (initial charge of zero). Since we know that the final charge on sphere W is 16e, we can conclude that the charge acquired from sphere A is also 16e.
2. Sphere W is touched to sphere B (initial charge of -26e): Once again, sphere W gains or loses charge from sphere B. Since the initial charge on sphere B is -26e, the charge acquired or lost by sphere W can be calculated as -26e + 16e = -10e.
3. Sphere W is touched to sphere C (initial charge of 46e): Similarly, the charge acquired or lost by sphere W can be calculated as 46e + 16e = 62e.
Now we need to determine the initial charge on sphere A. Since we know that after the interactions, sphere W has a final charge of 16e and it acquired 16e from sphere A, we can infer that the initial charge on sphere A was also 16e.
Hence, the multiple of e that gives the initial charge on sphere A is 16.