# Electrostatics Deflection Problem

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1. Sep 23, 2015

### Callix

The problem statement, all variables and given/known data
In inkjet printing, a rapidly moving nozzle horizontally squirts drops of ink that form letters and images on paper. A common problem is horizontal white lines running through the print due to a clogged nozzle. Another common problem is paper dust.

(a) Within the context of electrostatics, explain why paper dust can cause an inkjet printer to malfunction.
(b) Suppose the ink drops have a mass m = 2.00 x 10^-11 kg each and suppose the magnitude of the velocity at which they horizontally travel is 30 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 D = 2.20 x 10^-2 m, where there is a uniform vertical electric field with magnitude E = 8.6 x 10^4 N/C. If a drop is deflected a distance d = 3.30 x 10^-3 m, what magnitude of charge q does each drop acquire by the time it reaches the end of the deflection plate? The density of ink is 1,000 kg/m^3; assume the effects of gravity are negligible.

Possible relevant equations
y(t) = 1/2at^2
x(t) = vt
E = kQq/r^2
F = qE = ma

The attempt at a solution
(a)
. My thought process for this question was that there is a possibility that the dust particles are also charged in some manner. Therefore, the movement of these other outsider charges causes interference with the printer.
(b). I'm having a hard time picturing the drop passing through a charging unit and the deflection that occurs between the two parallel plates. I tried to look up diagrams in my textbook that depict a similarly described scenario, but there was nothing relevant. I also have a feeling that I'm going to have to apply some kinematic equations to also be able to solve part of this question.

Any help would be greatly appreciated! :)

Last edited: Sep 24, 2015
2. Sep 24, 2015

### Callix

This problem has been solved :)