Operation of an Inkjet Printer In an inkjet printer, letters and images are crea

Question

Operation of an Inkjet Printer

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 = 25.0 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 = 2.25 cm , where there is a uniform vertical electric field with magnitude E = 8.20×104 N/C . (Figure 1)

Part A

If a drop is to be deflected a distance d = 0.330 mm by the time it reaches the end of the deflection plate, what magnitude of charge qmust 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.

Hints

Operation of an Inkjet Printer

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 = 25.0 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 = 2.25 cm , where there is a uniform vertical electric field with magnitude E = 8.20×104 N/C . (Figure 1)

Part A

If a drop is to be deflected a distance d = 0.330 mm by the time it reaches the end of the deflection plate, what magnitude of charge qmust 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.

Hints

Explanation / Answer

Solution:

Here;

The time spent between the plates can be given as:

t = d / v (d= 2.25 cm = 0.0225 m)

=> t = 0.0225m / 25 m/s = 9×10-4 s

and the required acceleration to achieve the specified deflection can be given by:

a = 2d / t² (d= 0.33mm = 0.00033 m)

=> a = 2 * 0.00033 m / (9×10-4 s)2

=> a = 814.815 m/s2

Now,balancing the forces & according to the 2nd law of newton:

i.e, m×a = q×E (Considering drop to be in the shape of the ball/sphere throughout the process)
=> q = ma / E

=> q = 10-11kg × 814.815 m/s² / 8.2×104 N/C

=> q = 9.94 × 10-14 C

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