Electrostatic precipitators (ESP) are a common form of air-cleaning device. ESPs

Question

Electrostatic precipitators (ESP) 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 or 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 the (Figure 1) ). Air flows across the charged grid of wires and then passes between the stack of plates. A large negative potential difference (tens of thousands of volts) is applied between the wires and the plates, creating sparks that ionize 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. Part A Suppose a 1.8×106-kg dust particle with charge 6.5×109 C is moving vertically up a chimney at speed 6.0 m/s when it enters the +2000-N/C E field pointing away from a metal collection plate of an electrostatic precipitator. If the particle is 1.9 cm from the plate at that instant. Find the vertical distance the dust particle will move before hitting the plate.

Explanation / Answer

Electrostatic force F = Eq

    = 2000*6.5*10^-9 = 1.3 * 10^-5 N

acceleration a = F/m = 1.3*10^-5/1.8*10^-6 = 7.22 m/s

time required to stick is t, then

s = 0.5at^2

0.019 = 0.5*7.22 t^2

t = 0.0725 s

vertical height is given by

h = vt = 0.435 m   = 43.5 cm

Hence vertical distance is 43.5 cm

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