Chapter 18, Problem 1FC

To determine

The number of electrons must be transferred to have the same charge in both objects.

Answer to Problem 1FC

The number of electrons to be transferred is $\underset{\_}{1.9\times {10}^{13}}$.

Explanation of Solution

Calculation:

There are two objects carrying the different charges that are $-8.0\mu \text{C}$, $-2.0\mu \text{C}$.

Find equivalent charge of $-8.0\mu \text{C}$, $-2.0\mu \text{C}$.

$\begin{array}{c}\text{Equivalent}\text{charge}=\frac{-8.0\mu \text{C}+2.0\mu \text{C}}{2}\\ =-3.0\mu \text{C}\end{array}$

Each of the electrons has a value of charge. Mathematically, one electron has $1.60\times {10}^{-19}\text{C}$ of charge.

Calculate the electrons required for one Coulomb of charge.

$\begin{array}{l}1\text{electron}=1.60\times {10}^{-19}\text{C}\\ 1\text{C}=\frac{1}{1.60\times {10}^{-19}}\text{electrons}\\ 1\text{C}=6.25\times {10}^{18}\text{electrons}\end{array}$

The number of electrons to be transferred is,

$\begin{array}{c}\left(6.25\times {10}^{18}\right)\left(3.0\times {10}^{-6}\right)=1.875\times {10}^{13}\\ \cong 1.9\times {10}^{13}\end{array}$

Conclusion:

Thus, the number of electrons to be transferred is $\underset{\_}{1.9\times {10}^{13}}$.