Answer to Question #315397 in Electricity and Magnetism for pia

Question

Consider a soot particle of mass m_soot = 1.0 nanogram (=1.0 x 10^-9 g = 1.0 x 10^-12 kg), which corresponds to a diameter of a few microns. Some number of electrons have been added to give the particle a total charge q_soot, suppose the collector has a total charge of q_collector = 1.0 x 10^-6 C and is small enough to be treated as a point charge at the rim of the smokestack. (a) if the separation between the collector and the soot particle is r = 0.10 m, what is the value of q_soot so that the electric force exerted on the particle is equal to its weight? (b) How many electrons must be added to the soot particle?

Answer 1

a)

$\frac{kq_cq_s}{r^2}=mg,$

$q_s=\frac{mgr^2}{kq_c}=1.09\cdot 10^{-17}~C,$

b)

$n=\frac{q_s}e=68.$