An object carries a charge of -7.8 µC, while another carries a charge of -2.0 µC. How many electrons must be transferred from the first to the second object so that both objects have the same charge?
clearly, half the difference between the charges: (7.8-2.9)/2 = 2.9µC
So, how many electrons is that?
To determine the number of electrons that need to be transferred from one object to another, we need to use the fundamental unit of charge associated with electrons, which is the elementary charge, denoted as "e". The value of the elementary charge is approximately 1.6 × 10^(-19) coulombs.
First, let's convert the given charges of the objects from microcoulombs (µC) to coulombs (C):
For the first object: -7.8 µC = -7.8 × 10^(-6) C
For the second object: -2.0 µC = -2.0 × 10^(-6) C
Now, let's find the difference between the charges of the two objects. We can do this by subtracting the charge of the second object from the charge of the first object:
Charge difference = -7.8 × 10^(-6) C - (-2.0 × 10^(-6) C)
= -7.8 × 10^(-6) C + 2.0 × 10^(-6) C
= -5.8 × 10^(-6) C
Since electrons carry a negative charge, we need to transfer a specific number of electrons to make the charge difference equal to zero.
The charge carried by one electron (e) is approximately -1.6 × 10^(-19) C. To find the number of electrons, we divide the charge difference by the charge carried by one electron:
Number of electrons = Charge difference / Charge carried by one electron
= (-5.8 × 10^(-6) C) / (-1.6 × 10^(-19) C)
= (5.8 / 1.6) × (10^(-6) / 10^(-19))
= 3.625 × 10^(13) electrons
Therefore, approximately 3.625 × 10^(13) electrons must be transferred from the first object to the second object so that both objects have the same charge.