The ink drops have a mass m 1.00x10-11 kg each and leave the nozzle and travel h

Question

The ink drops have a mass m 1.00x10-11 kg each and leave the nozzle and travel horizontally toward the paper at velocity u = 17.0 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 Do 2.30 cm, where there is a uniform vertical electric field with magnitude E-7.90 104 N/C. (Figure 1) Constants| Periodic Table 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. Part A If a drop is to be deflected a distance d = 0.350 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 Express your answer numerically in coulombs View Available Hint(s) gure 1 of 1 Submit ious Ans Incorrect. Try Again: 4 attempts remaining Provide Feedback Next >

Explanation / Answer

Remember that the force experienced by the drop is equal to:

F = qE

Since F = ma, we also know that:

ma = qE

and:

a = qE/m

Now we can use the acceleration to find the change in position (deflection):

x = 1/2at2

x = 1/2 * (qE/m) * t2

And we can use this to find q:

x = 1/2 * (qE/m) * t^2

2x / (t^2) = qE/m

q = (2 * x * m) / (E * t^2)

Since the plates are 2.3cm long, the time will be:

t = 0.023 m / 17 m/s

t = 0.0013529s

Therefore:

q = (2 * d * m) / (E * t^2)

q = (2 * 0.00035 * (1*10^-11)) / ((7.9*10^4) * (0.0013529^2))

q = 4.84*10^-14 C

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