In an inkjet printer, tiny drops of ink of inertia m are given a charge q and th

Question

In an inkjet printer, tiny drops of ink of inertia m are given a charge q and then fired toward the paper at speed v. They first pass between two charged plates of length that create a uniform electric field of magnitude E between them (Figure 1) . 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.

Derive an expression for how far in the vertical direction a drop is deflected as it passes between the plates. Use the notation l for the length of the plates .

y = ( (l^2) / (2v^2) ) (qE / m - g)

A. For a drop inertia of 1.0×1010 kg , an electric field strength of 1.4×106 N/C , a plate length of17 mm , and a drop speed of 25 m/s , calculate the drop charge necessary to result in a deflection of 1.3 mm.

___________C

Explanation / Answer

along horizantal

x = vx*t

l = v*t

t = l/v

along vertical

Eq - mg = m*ay

ay = Eq/m - g

ay = Eq/m

displacement

dy = vy*t + (1/2)*ay*t^2

dy = (1/2)*(Eq/m - g)*(l^2/v^2)

dy = (l^2/2v^2)*(Eq/m - g)

+++

1.3*10^-3 = ((17*10^-3)^2/(2*25^2))*((1.4*10^6*q/10^-10)-9.8)

q = 4.023*10^-13 C

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