A particular inkjet printer uses electrostatic forces to direct droplets of ink

Question

A particular inkjet printer uses electrostatic forces to direct droplets of ink to create letters, words, and images at a resolution of 300 dots per inch. The figure below shows a schematic of the process. Using ultrasound, 100,000 droplets of ink are produced per second out of the droplet gun in the inkjet's head, which moves across the page horizontally. Each drop has a diameter of 72 m and moves at 20 m/s. Vertical displacement of the drops is achieved by placing a charge on each drop with an electron gun and then deflecting the drop through a uniform electric field provided by charged parallel plates.

(a) Assume ink has a density equal to that of water (1,000 kg /m3). What is the mass of each drop? kg

(b) Each ink drop is sprayed with electrons until it has a charge of 660 nC. How many excess electrons does that correspond to? electrons

(c) A particular drop experiences an electric field of 135 N/C as it passes through the 0.50-mm-long parallel plates. How much is it displaced vertically as it leaves the plates? (Give the magnitude.) m

(d) What is the vertical component of velocity as it leaves the plates? (Give the magnitude.) m/s

(e) If the plates are not charged, the drop would land in the center of the paper, which is an additional 1.5 mm away from the plates. How far below this point does the drop strike the paper?

Explanation / Answer

part a

m = V = 1000 * (4/3)(36*10-6)3 =1.9543*10-10 Kg

part b

number of electron =total charge /electron charge= -660*10-9/(1.6*10-19) =4.125*1012 electron

part c

acceleration a = force / mass = q*E / m

a=625*10-9 * 135 / 1.9543*10-10 =431740.265 m/s2

time between plates t = d / v = 0.00050/ 20 = 2.5*10-5 s

vertical displacement h = vi +½at² = 0+0.5*431740.265*(2.5*10-5)2= 13.49*10-5m=0.1349mm

part d

Vy = a*t = 431740.265* 2.5*10-5 =10.7935m/s

part e

time taken for additional 1.5mm let say tadd

additional time tadd= 0.0015 / 20 = 7.5*10-5 s

distnace of point of fall of drop strike at paper = h + Vy*tadd=13.49*10-5m +10.7935*7.5*10-5 =94.44125*10-5m

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