In a inkjet printer, letters and images are created by squiriting drops of ink h

Question

In a inkjet printer, letters and images are created by squiriting drops of ink horizontally at a sheet of paper from a rapidly moving nozzle. The pattern on the paper is controlled by an electrostatic valve that determine at each nozzle positon whether ink is squirted onto the paper or not. The ink drops have a mass m= 1.00*10^-11 kg each and leave the nozzle and travel horizontally toward the paper at velocity v= 20.0 m/s. The drops pass through a charging unit that gives each drop a positive charge q by causing it to lose some electrons. The drops then pass between parallel deflecting plates of length D_0 = 1.75 cm, where there is a uniform vertical electric field with magnitude E = 7.70*10^4 N/C. (Figure 1) If a drop is to be deflected a distance d = 0.320 mm by the time it reaches the end of the deflection pate, what magnitude of charge q must be given to the drop? Assume that the density of the ink drop is 1000 kg/m_3, and ignore the effects of gravity. Express your answer numerically in coulombs.

Explanation / Answer

motion parallel to plates:
D0 = (v)(t)
t = D0 / v [1]

motion perpendicular to plates:
d = at^2 / 2 [2]

Substitute [1] into [2]:
d = a(D0 / v)^2 / 2 [3]

The ink drop will be accelerated by the electric field between the plates:
a = F/m
a = qE/m [4]

Substituting [4] into [3]:
d = (qE/m)(D0 / v)^2 / 2
q = 2mdv^2 / [E(D0)^2]

q = 2(1.00e-11 kg)(3.20e-4 m)(20.0 m/s)^2 / [(7.70e4 N/C)(1.75e-2 m)^2]
q = 1.89e-7 C

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