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 1.20cm long, and drops of mass 0.12nanograms enter the electric field region moving horizontally at 16m/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

Vertical accel. of charge .. .. a = F/m = qE /m
a = q x 1.50^6N/C / 0.12^-12kg .. .. .. a = q (1.25^19) m/s² ---- (1)

Time between plates .. t = 0.012m / 16m/s .. .. t = 0.00075 s ---- (2)

Vert.displacement .. d = ut + ½ at²
0.50^-3m = 0 + (½ x q (1.25^19) x (0.00075)²

q = 0.50^-3 / 7.97^11 ..

q = 1.42^-16 C
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b)
Find vertical vel .the drop has at end of plates ..Vv = a.t ..(constant vel until it hits paper)
a = (1.42^-16) x ((1.25^19) m/s².. .. from equ (1)
t = 3.53^-4 s .... from equ (2)

Now find the displacement (D) on the paper.
D = 0.50mm [0.50^-3m] (starting displacement at end of plates) + (Vv x t') ..
where t' = time to reach paper .. (0.50cm [0.50^-2m] / 16m/s)

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