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 34.0 m diameterdrops of ink, charges them by spraying 800,000 electrons on the surface, and shoots them toward the page with a horizontal velocity of 23.0 m/s. Along the way, the drops pass through the long axis of two horizontal, parallel electrodes that are 6.0 mm long, 4.0 mm wide, and spaced 1.0 mmapart. The distance from the center of the electrodes to the paper is 2.80 cm . To form the letters, which have a maximum height of 6.0 mm, the drops need to be deflected up or down a maximum of 3.0 mm. Ink, which consists of dye particles suspended in alcohol, has a density of 800 kg/m3.

What electric field strength is needed between the electrodes to achieve this deflection?

Explanation / Answer

here,
distance betweent he electrode, d = 1 mm = 0.001 m

velocity of sparay, v = 23 m/s

From third eqn of motion,

v^2 = 2*a*s

solving for acceleration till mid of plate

a = v^2/2(s/2)
a = 23^2/(0.001)
a = 5.29*10^5 m/s^2

Now From Newton Second , F = m*a
also Electric force, F = qE

so
qE = m*a

solving for Electric field , E
E = m*a/q
Where,
m is mass of electron
q = charge on electron

E = (9.109*10^-31 * 5.29*10^5) /(1.6*10^-19)
E = 3.012*10^-6 N/C

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