Question

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 1

The magnitude of charge q can be found by equating the electric force to the gravitational force, and solving for q. The number of electrons needed is determined by dividing the magnitude of charge by the charge of one electron.

Step-by-step explanation:

To find the magnitude of charge q (in units of C) for which the electric force exerted on a particle equals its weight (mg), we set the electric force equal to the gravitational force. Using Coulomb's law, the electric force F is F = k * |qQ| / r², where k is the Coulomb's constant (9 x 10⁹ N m²/C²), q is the charge we want to find, and Q and r are the charge and distance related to another charged object causing the electric force. The gravitational force is mg, where m is the mass of the particle and g is the acceleration due to gravity (10 m/s²). Setting F = mg, we solve for q and get q = mgr² / (kQ).

To determine how many electrons must be added to the soot particle, we divide the magnitude of charge q by the elementary charge e (the charge of one electron, 1.6 x 10⁻¹⁹ C). The number of electrons, n, is given by n = q/e.

Answer 2

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

Step-by-step 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)