In an inkjet printer tiny drops of ink of inertia m are give

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 Ebetween 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.

a) 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 ?. Express in terms of the variables m, q, v, l, E, and acceleration due to gravity g.

b) For a drop inertia of 1.4×10^?10 kg , an electric field strength of1.4×10⁶ N/C , a plate length of 17 mm , and a drop speed of 25 m/s , calculate the drop charge necessary to result in a deflection of 1.3 mm.

c) Is it acceptable to ignore the effects of gravity in this case?

Solution

The acceleration is

F=qE

ma+mg=qE

a=( qE/m )-g

The horizontal distance is

l =vot

Thus the time is

t= l/vo

The vertical displacement is

dy=1/2 at^2

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

Substitute the given values in above equation and solve the charge

q=4.3×10^-10 C

In this case the value of qE/m value is very high compared to g value.

So in this case we neglect the gravitational effect