Electrostatic Printer and two plate capacitors deflecting charged ink droplets

AI Thread Summary
Electrostatic ink-jet printers use charged ink droplets that are deflected by electrodes to form letters on paper. The printer generates 30-μm droplets, charging them with 800,000 electrons and propelling them at 20 m/s. To achieve a maximum deflection of 3.0 mm within a 2 cm distance to the paper, calculations are needed for the required charge on the electrodes and the time taken for droplets to reach the paper. The discussion highlights the need to understand the relationship between charge, electric field, and the resulting motion of the ink droplets. The trajectory of the droplets is influenced by the electric field, resembling a parabolic path due to the acceleration experienced between the plates.
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Homework Statement



One type of ink-jet printer, called an electrostatic ink-jet printer, forms letters by using deflecting electrodes to steer charged ink drops up and down vertically as the ink jet sweeps horizontally across the page. The ink jet forms 30-μm-diameter drops of ink, charged them by spraying 800,000 electrons on the surface, and shoots them toward the page at a speed of 20 m/s. Along the way, the drops pass through two parallel electrodes that are 6.0 mm long, 4.0 mm wide, and spaced 1.0 mm apart. The distance from the center of the plates to the paper is 2.0 cm. To form the letters which have a maximum hieght of 6.0 mm, the drops need to be deflected up or down at maximum if 3.0 mm. Ink, which consists of dye particles suspended in alcohol, has a density of 800 kg.m^3

What amount of charge is needed on each electrode to produce this electric field

Homework Equations

The Attempt at a Solution



I know qE/m, I found m and q and also E via part A I solved, but now I'm stumped, can anyone give me hand?
 
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How long will a drop take to reach the paper? What vertical velocity will it need to achieve the desired deflection? How long does it have to acquire that velocity? What acceleration does that imply?
 
Doesn't it follow a parabolic trajectory between the plates, sort of acting like a stronger gravitational field?
 
Basic_Physics said:
Doesn't it follow a parabolic trajectory between the plates, sort of acting like a stronger gravitational field?
Sure, but most of the deflection (in terms of distance, as opposed to angle) will occur across the 2cm gap to the paper.
 
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