in an inkjet printer, letters are built up by squirting drops of ink at the pape

Question

in an inkjet printer, letters are built up by squirting drops of ink at the 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 radius of 20.0m and leave the nozzle and travel toward the paper at a velocity of 25.0m/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 2.35cm where there is a uniform vertical electric field with a magnitude of 7.60

Explanation / Answer

Start with density = m/V

V = 4/3pi(r3) = 4/3(pi)(20 X 10-6)3 = 3.351 X 10-14 m3

1000 = m/(3.351 X 10-14)

m = 3.351 X 10-11 kg

Then we need the time required to go through the plates.

d = vt

.0235 = 25(t)

t = 9.4 X 10-4 s

Then we can find the necessary acceleration to deflect

d = vot + .5at2

.35 X 10-3 =0 + .5a(9.4 X 10-4)2

a = 792.2 m/s2

Finally apply F = ma and F = qE together

ma = qE

(3.351 X 10-11)(792.2) = q(7.6 X 104)

q = 3.49 X 10-13 C

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