What is the magnitude of qsoot (in units of C) so that the electric force exerted on the particle is equal to its weight = mg?.

Use: g = 10 m/s², and k = 9E9 N m²/C².

How many electrons must be added to the soot particle?

Answer: In the exercise there are lost data, but I already found the exercise in a book

qsoot = 6.66e-18

no. electrons = approximately 42 electrons

Explanation:

msoot = 1.2e-12 kg

qcollector = 2e-06 C

rcollector = 0.1 m

The electric force must be equal to the weigth, so:

W=msoot*g (1)

Felec = k*qsoot*qcollector/r^2 (2)

equaling (1) and (2):

msoot*g = k*qsoot*qcollector/r^2 (3)

reorganizing the equation (3) and clear qsoot:

qsoot = (msoot*g*r^2) / (k*qcollector)

qsoot = 6.66e-18

no. electrons = qsoot / qelectron

no electrons = 41.6 electros (approximately 42 electrons)