An object carries a charge of -6.4 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?
if the total charge is -8.4 µC , then each will have -4.2 µC, so it appears that 2.2 µC has to be transfered
Number electrons=2.2 e-6 C/1.6e-19 C=1.37500e13 electrons
check that.
-6.4 + x = -2.0 - x
2 x = 4.4
x = 2.2
so I must add a charge of +2.2*10^-6
and end up with
-4.2*10^-6 on each
now each electron has charge of - 1.6*10^-19 C
so + 2.2*10^-6 = -n (-1.6*10^-16)
( the -n is because I need to subtract a negative charge to get a +x)
n = (2.2 / 1.6) *10^10
Sorry, used 10^-16 instead of 10^-19
should be
(2.2 / 1.6) 10^13
To find out how many electrons must be transferred from the first object to the second object, we need to determine the difference in charges between the two objects and then calculate the number of electrons associated with this charge difference.
The charge on an electron is given by the elementary charge, which is approximately -1.6 x 10^-19 Coulombs (C).
First, let's find the charge difference between the two objects:
Charge of the first object = -6.4 µC = -6.4 x 10^-6 C
Charge of the second object = -2.0 µC = -2.0 x 10^-6 C
Charge difference = Charge of the second object - Charge of the first object
= (-2.0 x 10^-6 C) - (-6.4 x 10^-6 C)
= -2.0 x 10^-6 C + 6.4 x 10^-6 C
= 4.4 x 10^-6 C
Now, let's calculate the number of electrons associated with this charge difference:
Number of electrons = Charge difference / Charge on an electron
= (4.4 x 10^-6 C) / (-1.6 x 10^-19 C)
≈ -2.75 x 10^13
Since the charge on an electron is negative, the negative sign indicates that electrons need to be transferred from the first object to the second object. Therefore, approximately 2.75 x 10^13 electrons need to be transferred from the first object to the second object so that both objects have the same charge.