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 1.00cm long, and drops of mass 0.12nanograms enter the electric field region moving horizontally at 17m/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



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Explanation / Answer

relevant equations

1) t = D0 / v

2) d = ( a * t^2 ) / 2

3) F = m * a

4) F = E * Q

Time travelled in electric field = 1cm/17m/s = 5.8823 E -4

deflection D = [(E*Q)/m]*t2/2 = 0.5 mm

Q = 2.312 E -10 C

Velocity at the end = V = [(E*Q)/m].t = 1700 m/s

Time taken to strike the paper = (.50E-2)/17 = 2.941 E-5 sec

vertical deflection when it strikes the paper = vt = 1700 * 2.941 E-5 = .005 m = 5 cm

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