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 16.0 micro meter and leave the nozzle and travel toward the paper at a velocity of 19.0 {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 1.55 cm where there is a uniform vertical electric field with a magnitude of 7.90×104 {N/C}.

If a drop is to be deflected a distance of 0.330 {mm} by the time it reaches the end of the deflection plate, what magnitude of charge must be given to the drop? (Assume that the density of the ink drop is 1000kg/m^3).

I do not know ever where to begin.

Explanation / Answer

Mass of the ink drop m = ? V = 1000 * (4/3) p (16 x 10-6)3 = 1.71 x10-11 kg Time taken to travel 1.55 cm is t = 0.01550 / 19 =0.81 ms The acceleration of the drop a = 2 s /t2 = 2 * 0.33 x 10-3/ 0.81 * 0.81 x 10-6 = 1005.9 m/s2 The charge of the drop q = m a / E = 1.71 x 10-11 * 1005.9 / 7.90 x 104 =217.73 x 10-15 C

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