Chapter 18, Problem 71RPP

Electrostatic precipitator (esp) Electrostatic precipitators are a common form of air-cleaning device ESPs are used to remove particle emissions from smoke moving up smokestacks in coal and oil-fired electricity-generating plants and pollutants from the boilers in oil refineries. You can buy portable ESPs of whole-house ESPs that connect to the cold-air return on the furnace. These devices remove about 95% of dirt and 85% of microscopic particles from the air.

A basic electrostatic precipitator contains a negatively charged horizontal metal grid (made of thin wires) and a stack of large flat, vertically oriented metal collecting plates, with the plates typically spaced about 1 cm apart (only two plates are shown in Figure 18.30). Air flows across the charged grid of wires and then passes between the plates. A large negative potential difference (tens of thousands of volts) is applied between the wires and the plates, creating a strong electric field that ionizes particles in the air around the thin wires. Negatively charged smoke particles flow upward between the plates. The charged particles are attracted to and stick to the oppositely charged plates and are thus removed from the moving gas.

Suppose a $\text{2}\text{.0 }\times {\text{ 10}}^{\text{-}}{}^{\text{6}}\text{-kg}$ dust particle with charge $\text{-4}\text{.0 }\times {\text{ 10}}^{-}{}^{\text{9}}\text{C}$ is moving vertically up a chimney at speed 6.0 m/s when it enters the $\text{+2000 - N/C}\stackrel{\to }{E}$ field near the metal collecting plate, pointing perpendicularly to the plate. If the particle is 2.0 cm from the plate at that instant, which answer below is closest to the magnitude of its horizontal acceleration toward the plate?

a. $\text{2}\text{.0 }\times {\text{ 10}}^{\text{-}}{}^{\text{5}}{\text{m/s}}^{\text{2}}$

b. $\text{1}\text{.2 }\times {\text{ 10}}^{\text{-4}}{\text{m/s}}^{\text{2}}$

c. $\text{4}\text{.0 }\times {\text{ 10}}^{\text{-4}}{\text{m/s}}^{\text{2}}$

d. $\text{4}{\text{.0 m/s}}^{\text{2}}$

e. ${\text{24 m/s}}^{\text{2}}$