As a technical application of this type of motion, consider an ink jet printer.
ID: 3279839 • Letter: A
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As a technical application of this type of motion, consider an ink jet printer.
Question 5: As a technical application of this type of motion, consider an ink jet printer. The basic mechanism is that drops of ink, each with a radius of Y-20 m, are charged to q sprayed from a nozzle towards the page at an initial speed of 30 m/s. On the way to the paper, they pass a region with a uniform electric field of magnitude E between two charged plates which deflects them up or down. Assume that the distance from the center of the plates to the paper is d = 2.0cm. The maximum height of a letter is 6 mm, i.e. the drops have to be deflected up or down 3 mm. What is the maximum electric field strength needed? Start by sketching the situation. Hint: There is one piece of information that you will have to estimate. 1.3 × 10-13 C andExplanation / Answer
Given. drop of ink, radius r = 20 micro m
charge on plates, q = 1.3*10^-13 C
initial speed, v = 30 m/s
distance to the center of the plates to the page, d = 2 cm
maximum height of letter, h = 6 mm
let the plate height be H and distance between the plates be D
now, force on the oil drop = QE [ where Q is charge on the oil drop ]
now the oil drop moves for vertical height H in the plates
so time spent inside the plates = t
H = vt + 0.5gt^2
4.9t^2 + 30t - H = 0
in this time, the particle has acquired a lateral velocity of u
u = QEt/m [ where m is mass of oil drop]
m = 4*pi*r^3*rho/3 [ where rho is density of ink]
now, distance covered laterally by ink in this time, x = 0.5*QE*t^2/m
and after this, distance covered laterally = ut'
where (d - H/2) = vt' - 0.5gt'^2
hence QEtt'/m + 0.5QE*t^2/m = 3*10^-3
QEtt'/m + 0.5QE*t^2/m = 3*10^-3
t, and t' and m can be found from previous equations, Q has to be approximated
and the E can be found
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