In an inkjet printer, tiny drops of ink of mass m are given a charge q by stripp

Question

In an inkjet printer, tiny drops of ink of mass m are given a charge q by stripping off some electrons, and then fired toward the paper at speed v. They first pass between two charged plates of length D that create a uniform electric field of magnitude E between them. The field direction is perpendicular to the plates and to the initial path of the drops. The electric field deflects each drop from its initial horizontal path and is used to control what is printed on the paper. (a) Derive an expression for how far in the vertical direction a drop is deflected (d) as it passes between the plates. Ignore gravity. (b) For a drop mass of 1.0 x 1010 kg, an electric field strength of 1.4 x 106 N/C, a plate length of 20mm, and a drop speed of 300 m/s, calculate the drop charge necessary to result in a deflection of 1.0 mm. (c) Why is it ok to ignore gravity? Use some specific numbers to make your case.

Explanation / Answer

(A) t = D / v

and a = qE / m

in vertical, v0 = 0

d = u t + a t^2 /2

d = 0 + (q E / m) ( D / v)^2 / 2

d = ( q E D^2) / (2 m v^2)

(B) 1 x 10^-3 = (q x 1.4 x 10^6 x 0.020^2 ) / (2 x 1 x 10^-10 x 300^2 )

  
q = 3.214 x 10^-11 C

(C) due to field , a = q E / m = 4.5 x 10^10 m/s^2

and g = 9.8 m/s^2

hence it is ok to ignore gravity.

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