Question

Suppose a speck of dust in an electrostatic precipitator has 1.0000×10^12 protons in it and has a net charge of –5.00 nc (a very large charge for a small speck). how many electrons does it have?

Answer 1

Answer:

$1.0313\cdot 10^{12}$

Explanation:

The net charge is given by the sum of the charges of the protons and of the electrons:

$Q=N_p q_p + N_e q_e$

where we have

$Q=-5.00 nC=-5.00\cdot 10^{-9}C$ is the net charge

$N_p = 1.0\cdot 10^{12}$ is the number of protons

$q_p = +1.6\cdot 10^{-19}C$ is the charge of one proton

$N_e$ is the number of electrons

$q_e = -1.6\cdot 10^{-19}C$ is the charge of one electron

Solving the equation for $N_e$, we find the number of electrons:

$N_e = \frac{Q-N_p q_p}{q_e}=\frac{-5.0\cdot 10^{-9}C-(1.0\cdot 10^{12})(1.6\cdot 10^{-19}C)}{-1.6\cdot 10^{-19}C}=1.0313\cdot 10^{12}$