Question

A plate carries a charge of 3.8 UC, while a rod carries a charge of 1.9 C. How many electrons must be transferred from the plate to the rod, so that both objects have the same charge?

Answer 1

To find the number of electrons transferred from the plate to the rod, calculate the difference in charge between them and divide it by the charge of an electron.

Step-by-step explanation:

To determine how many electrons must be transferred from the plate to the rod so that both objects have the same charge, we need to calculate the difference in charge between them. The plate carries a charge of 3.8 microcoulombs (UC) and the rod carries a charge of 1.9 coulombs (C). To convert the rod's charge to microcoulombs, we multiply it by 10^6 (since 1 C = 10^6 UC):

Final charge of rod = 1.9 C x 10^6 = 1.9 x 10^6 UC

Now, we can calculate the difference in charge and convert it to the number of electrons:

Difference in charge = Final charge of rod - Charge of plate = 1.9 x 10^6 UC - 3.8 UC = 1.9 x 10^6 UC - 3.8 UC = 1.8962 x 10^6 UC

Since the charge of an electron is approximately -1.6 x 10^-19 C, we can determine the number of electrons required:

Number of electrons = Difference in charge / Charge of an electron = 1.8962 x 10^6 UC / (-1.6 x 10^-19 C) ≈ -1.1851 x 10^25 electrons

Answer 2

`N_(electrons)=Q_(transfered)/q_(electron)=5.94*10^(18)electrons`

Step-by-step explanation:

The total charge is distributed over the two objects:

`Q_(total)/2=(3.8*10^(-6)C+1.9C)/2=0.9500019C\\`

The plate and the rod must have
`Q_(total)/2\\`. So the charge transferred from the plate to the rod is:

`Q_(transfered)=3.8*10^(-6)C-Q_(total)/2=3.8*10^(-6)C-0.9500019C=-0.9499981C\\`

Number of electrons:

`N_(electrons)=Q_(transfered)/q_(electron)=-0.9499981C/(-1.6*10^(-19)C)=5.94*10^(18)electrons`