In an inkjet printer, letters are built up by squirting drops of ink at the pape
ID: 2282573 • Letter: I
Question
In an inkjet printer, letters are built up by squirting drops of ink at the paper from a rapidly moving nozzle. The ink drops, which have a mass of 1.3 10-8 g each, leave the nozzle and travel toward the paper at 21 m/s, passing through a charging unit that gives each drop a positive charge q by removing some electrons from it. The drops then pass between parallel deflecting plates 2.0 cm long where there is a uniform vertical electric field with magnitude 7.7 104 N/C. If a drop is to be deflected 0.31 mm by the time it reaches the end of the deflection plates, what magnitude of charge must be given to the drop?'
_____C
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(1.3e-11 kg)(3.10e-4 m)(21.0 m/s)^2 / [(7.70e4 N/C)(2e-2 m)^2]
q = 115.4e-15 C
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