In an inkjet printer, letters and images are created by squirting drops of ink h

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

m = 1.00×1011 kg each and leave the nozzle and travel horizontally toward the paper at velocity v = 22.0 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 D0 = 1.80 cm , where there is a uniform vertical electric field with magnitude E = 8.50×104 N/C .

(A) If a drop is to be deflected a distance d = 0.270 mm by the time it reaches the end of the deflection plate, what magnitude of charge q must be given to the drop? Assume that the density of the ink drop is 1000 kg/m3 , and ignore the effects of gravity.

Explanation / Answer

q = charge on the drop

V = horizontal speed = 22 m/s

Do = length of deflecting plates = 1.80 cm = 0.018 m

t = time taken to reach the end of deflection plate = Do / V = 0.018 / 22 = 8.2 x 10-4 sec

E = electric field = 8.50 x 104 N/C

deflecting force by the electric field is given as

F = qE

hence the acceleration of the drop due to electric force is given as

a = F/ m = qE/m = q (8.5 x 104) / (1 x 10-11)

d = deflection = 0.270 mm = 0.27 x 10-3 m

Vo = initial speed in the direction of deflection = 0

using the equation

d = Vo t + (0.5) a t2

0.27 x 10-3 = (0) (8.2 x 10-4 ) + (0.5) (q (8.5 x 104) / (1 x 10-11)) (8.2 x 10-4 )2

q = 9.45 x 10-14 C

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