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

Question

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 patted on the paper is controlled by an electrostatic valve that determines at each nozzle position whether ink is squirted onto the paper or not. Figure 1 The ink drops have a mass m = 1.00 times 10^-11 kg each and leave the nozzle and travel horizontally toward the paper at velocity upsilon = 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 D_0 = 2.50 cm, where there is a uniform vertical electric field with magnitude E = 8.50 times 10^4 N/C. 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 q must be given to the drop? Assume that the density of the Ink drop is 1000 kg/m^3, and ignore the effects of gravity. Express your answer numerically in coulombs.

Explanation / Answer

m= mass = 1*10-11 kg

v= velocity = 25 m/s

length of plates or distance travelled ,D0 = 2.50 cm

E = electric field = 8.50*104 N/C

d = vertical distance = 0.330mm

q= charge = ?

p= density = 1000 kg/m3

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a= acceleration

F( force) = ma

also F= q*E

so ma= q*E

a = q*E / m

a= q* 8.50*104 / 1*10-11 = 8.5*1015 *q   m/s2

time to travel D0, t= D0 / v

t= 2.50*10-2 / 25 = 1*10-3 s

in y- direction, S= u*t + (1/2)*a*t2

S= d, u= initial velocity in y- direction = 0

d= 0+ (1/2)*a*t2

0.330*10-3 = (1/2)*8.5*1015 *q *( 1*10-3)2

q= 7.764*10-14 C

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