Four identical metallic objects carry the following charges: +1.46, +6.39, -4.06, and -9.94C. The objects are brought simultaneously into contact, so that each touches the others. Then they are separated. (a) What is the final charge on each object? (b) How many electrons (or protons) make up the final charge on each object?
I know for (a) you just add them and divide by the number of them, so four. But I can't figure out the last one. I thought you take what you get from (a) and divide by 1.6x10^-19, but for some reason I cannot get it right!
To find the final charge on each object, you are correct that you add the charges together and divide by the number of objects. In this case, there are four objects. So, the final charge on each object would be:
Total charge = +1.46C + +6.39C + (-4.06C) + (-9.94C)
Total charge = -5.15C
Final charge on each object = Total charge / Number of objects
Final charge on each object = -5.15C / 4
Final charge on each object = -1.2875C
For part (b) - determining how many electrons or protons make up the final charge on each object - you are correct that you need to divide the charge by the elementary charge, which is approximately 1.6 x 10^-19 C.
Number of electrons (or protons) = Final charge / Elementary charge
Number of electrons (or protons) = -1.2875C / 1.6 x 10^-19 C
Now, let's do the calculation:
Number of electrons (or protons) = -1.2875C / (1.6 x 10^-19 C)
Number of electrons (or protons) ≈ -8.0469 x 10^18 electrons (or protons)
It means that the final charge on each object corresponds to approximately -8.0469 x 10^18 electrons (or protons).
To find the final charge on each object after bringing them into contact and then separating them, you are correct in adding up the charges on all four objects and dividing by four. This will give you the average charge on each object.
For part (a), let's calculate the final charge:
+1.46C + +6.39C + (-4.06C) + (-9.94C) = -6.15C
Now, to determine the final charge on each object, divide the total charge by the number of objects:
-6.15C / 4 objects = -1.5375C
Therefore, the final charge on each object is approximately -1.54C.
For part (b), you need to determine how many electrons (or protons) make up this final charge on each object. To do this, you can use the elementary charge, which is approximately 1.6x10^-19C.
Divide the final charge by the elementary charge to find the number of elementary charges:
-1.54C / (1.6x10^-19C) = -9.625x10^18 elementary charges
Since the calculated result is negative, it means that the objects have an excess of electrons compared to neutrality. Note that when dividing the charges by the elementary charge, any resulting decimals are considered insignificant for this question.
Hence, the final charge on each object is approximately -1.54C, and the number of electrons (or protons) making up this charge is approximately -9.625x10^18.