Question

An electroscope has a charge of −3.9 µC while your finger has a charge of 4.2 µC. You touch the electroscope with your finger and discover that the charges of your finger and the electroscope are now the same. In this process, electrons were transferred from the electroscope to your finger. How many electrons were transferred in order for your finger and the electroscope to have the same charge?

---I got 4.05 but this isn't right

Answer 1

Consider the in the final state, the electroscope and you are the whole system and use the conservation of total charge. At the end, you both have equal charge, you may say Qf on the electroscope and Qf on your finger, have a total charge of 2Qf.

The total charge from the initial system is −3.9 µC + 4.2 µC. = 0.3 µC

Conservation of charge says Final Total Charge = Initial Total Charge
2Qf = 0.3 µC
Qf = 0.15 µC

Since your finger started with 3.6 µC, and now has 0.15 µC,
Q_transfer = Qf-Qi = 0.15 - 4.2 = -4.05 µC

EDIT:

I answered with the total charge transferred, but the numbers of electrons were not spcified.

To convert the charge in Coulombs to electrons, you need to use the following rule:

1 e = 1.602x10^-19 C     Then, we're doing the conversion:

#e transferred = -4.05x10^-6 / 1.602x10^-19

#e transferred = -2.528x10¹³ electrons.

This should be the correct answer and not 2.53x10¹⁴ electrons. Try this value.