In an ink-jet printer, drops of ink are given a controlled amount of charge befo

Question

In an ink-jet printer, drops of ink are given a controlled amount of charge before they pass through a uniform electric field generated by two charged plates. If the electric field between the plates is 1.5x106N/C over a region 0.90cm long, and drops of mass 0.12nanograms enter the electric field region moving horizontally at 19m/s, (a) how much charge on a drop is necessary to produce a vertical deflection of 0.50mm at the end of the electric field? (b) What is the vertical deflection between the point where it leaves the plates and where it strikes the paper, if the paper is 0.50cm from the end of the charged plates? Ignore other forces such as gravity and air resistance, and assume the field between the plates is vertical and constant, and drops abruptly to zero at the edge of the plates.
(a)_____ C
(b)_____ cm

Explanation / Answer

E = 1.5 e6

m = 1.2 e-10

l = 9 e-3

v = 19

d = 5 e-3

let charge be q coulomb

horizontal velocity is always constant.

so,

19*t1 = 9 e-3 , t1 = 4.73684 e-4 sec

19*t2 = 5 e-3, t2 = 2.631579 sec

for vertical component,

uy = 0

t = t1

so,

vy = 0 + a*t

a = qE/m

so, vy = q*E*t1/m = q*5.92105 e12 m/s

 

vertical deflection,

dy = vy*t2

as there is no acceleration in y-direction now

dy = q*1.558171084 x 109 m

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