In an inkjet printer, letters and images are created by squirting drops of ink h
ID: 2270855 • Letter: I
Question
In an inkjet printer, letters and images are created by squirting 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 determines at each nozzle position whether ink is squirted onto the paper or not.
The ink drops have a mass ( exttip{m}{m}) = 1.0010?11({ m kg}) each and leave the nozzle and travel horizontally toward the paper at velocity ( exttip{v}{v}) = 21.0({ m m/s}) . The drops pass through a charging unit that gives each drop a positive charge ( exttip{q}{q}) by causing it to lose some electrons. The drops then pass between parallel deflecting plates of length ( exttip{D_{ m 0}}{D_0}) = 2.20({ m cm}) , where there is a uniform vertical electric field with magnitude( exttip{E}{E}) = 8.45104({ m N/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(1.0 * 10^-11 kg)(3.10 * 10^-4 m)(21.0 m/s)^2 / [(8.45 * 10^4 N/C)(2.20 * 10^-2 m)^2]
q = 2.7342 * 10^-12 / 1859
q = 1.47 * 10^-15 C
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