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

Question

An 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 = 1.0010?11kg each and leave the nozzle and travel horizontally toward the paper at velocity v = 20.0m/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 D(0) = 2.50cm , where there is a uniform vertical electric field with magnitude E = 8.10104N/C .

If a drop is to be deflected a distance d = 0.330mm 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 1000kg/m3 , and ignore the effects of gravity.

(Please shortly explain and give asnwer)

Explanation / Answer

The drop, neglecting gravity, will move with a parabolic trajectory.

In the X axis speed is constant, while the E field will induce a force, ie an acceleration on the drop

The X direction motion can be used to derive the time spent in the E field,

l=vt

thus

t=l/v

in the Y direction one has

d=1/2at2 the acceleration can be estimated by means of Newton

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