How Much Charge is Needed for an Ink Drop to Deflect in an Inkjet Printer?

[gp0015]

Homework Statement

In the somewhat ‘archaic’ inkjet printers, letters are built up by squirting drops of ink at the paper from a rapidly moving nozzle. The pattern on the paper is controlled by an electrostatic valve that determines at each nozzle position whether ink is squirted onto the paper or not. The ink drops, αr, in radius (here, α is a positive, dimensionless constant), leave the nozzle and travel toward the paper at v m/s. The drops pass through a charging unit that gives each drop a positive charge q when the drop loses some electrons. The drops pass between parallel deflecting plates d cm in length where there is a uniform vertical electric field with magnitude E N/C. If a drop is to be deflected β mm (here β is a positive number) by the time it reaches the end of the deflection plate, what magnitude of charge must be given to the drop? (Assume that the density of the ink drop is ρ kg/m3.)

Homework Equations

1) t = D0 / v

2) d = ( a * t^2 ) / 2

3) F = m * a

4) F = E * Q

The Attempt at a Solution

Having a lot of trouble...

 

[Liquidxlax]

Draw a triangle with a length d and a height beta. The x velocity is constant in this case, and there is an electric force acting on the drop in an upward direction and a gravitational force in the downward direction so

F_y = QE - mg = ma_y

and over a distance d it has moved up a distance beta

You need to figure out how long it takes for the drop to travel a distance d and figure out an equation for the acceleration upwards.

Then solve it in terms of q