Electrostatic precipitators use electric forces to remove pollutant particles from smoke, in particular in the smokestacks of coal-burning power plant

asked 2020-12-27
Electrostatic precipitators use electric forces to remove pollutant particles from smoke, in particular in the smokestacks of coal-burning power plants. One form of precipitator consists of a vertical, hollow, metal cylinder with a thin wire, insulated from the cylinder, running along its axis. A large potential difference is established between the wire and the outer cylinder, with the wire at lower potential. This sets up a strong radial electric field directed inward. The field produces a region of ionized air near the wire. Smoke enters the precipitation at the bottom, ash and dust in it pick up electrons, and the charged pollutants are accelerated toward the outer cylinder wall by the electric field. Suppose the radius of the central wire is 90.0 u(m,the radius of the cylinder is 14.0 cm, and a potential difference of 50.0 kG is established between the wire and the cylinder. Also assume that the wire and cylinder are both very long in comparison to the cylinder radius.
(a) What is the magnitude of the electric field midway between the wire and the cylinder wall? (V/m)
(b) What magnitude of charge must a 30.0 u(gas particle have if the electric field computed in part (a) is to exert a force ten times the weight of the particle? (c)

Expert Answers (2)




Best answer

a) Electric field is,

\(E=\frac{V_{ab}}{\ln(b/a)} \cdot \frac{1}{r}\)

\(E=\frac{59000v}{ln(0.125/0.00009)} \cdot \frac{1}{0.0625}\)

\(E=130454.14 \ V/m\)

\(E=1.3 \times 10^5 \ V/m\)

b)\(F=E \cdot q\)

\(10 \cdot m \cdot g=130454.14 \cdot q\)

\(q=\frac{(10 \cdot 0.00000003 \cdot 9.8)}{130454.11}\)

\(q=2.25 \times 10^{-11} \ C\)


expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-05-20
Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton any where along the tunnel or outside the ball. Let \(\displaystyle{F}_{{R}}\) be the magnitude of the electrostatic force on the proton when it islocated at the ball's surface, at radius R. As a multiple ofR, how far from the surface is there a point where the forcemagnitude is 0.44FR if we move the proton(a) away from the ball and (b) into the tunnel?
asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
asked 2021-04-22
Nerve cells are long, thin cylinders along which electric disturbances (nerve impulses) travel. The cell membrane if a typical nerve cell consists of an inner and outer wall separated by a distance of \(\displaystyle{0.10}\mu{m}\). The electric field within the cell membrane is \(\displaystyle{7.0}\cdot{10}^{{{5}}}\) N/C. Approximating the cell membrane as a parallel plate capacitor, determine the magnitude of the charge density on the inner and outer cell walls.
asked 2021-03-12
A 75.0-kg man steps off a platform 3.10 m above the ground. Hekeeps his legs straight as he falls, but at the moment his feettouch the ground his knees begin to bend, and, treated as aparticle, he moves an additional 0.60 m before coming torest.
a) what is the speed at the instant his feet touch theground?
b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?
c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.