One type of ink-jet printer, called an electrostatic ink-jet printer, forms the

Question

One type of ink-jet printer, called an electrostatic ink-jet printer, forms the 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 x 10-6 m diameter drops of ink, charges them by spraying 600,000 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 horizontal, parallel electrodes that are 6.0 mm long and 4.0 mm wide, and spaced 1.0 mm apart.  The distance from the centre of the electrodes to the paper is 2.0 cm.  To form the tallest letters, which have a height of 6.0 mm, the drops need to be deflected upward (or downward) by 3.0 mm.  What electric field strength (in N/C) is needed between the electrodes to achieve this deflection?  Ink, which consists of dye particles suspended in alochol, has a density of 800 kg/m3

Explanation / Answer

volume of droplet = (4/3)*pi*(diameter/2)^3 = (4/3)*pi*(30*10^-6/2)^3 = 1.413716694 * 10^-14 m^3

so.. mass of each droplet = volume * density = 1.413716694 * 10^-14 * 800 = 1.13097335529 * 10^-11 kg

charge of each drop = 600000 * charge of 1 electron = 600000 * 1.6 * 10^-19 = 9.6 * 10^-14 C

along the direction perpendicular to paper ...
speed = v = 20 m/sec
distance = 0.02 m

so. time taken to reach the paper = 0.02/20 = 0.001 sec

so.. along vertical ..
let the acceleration be a ...
u = inital sped = 0
t = 0.001
distance s = 3 mm = 0.003 m

s = ut + 0.5*a*t^2
0.003 = 0 + 0.5*a*0.001 ^2

so.. acceleraion of droplet = a = 6000 m/sec2

so.. force on droplet = mass * a = 6000*1.13097335529 * 10^-11 = 6.78584013174 * 10^-8 N

so... electric field = force / charge = ( 6.78584013174 * 10^-8) / (9.6 * 10^-14) = 706858.34705625 N/C

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