Question

In an inkjet printer, letters and images are created by squirting drops of ink horizontally at a sheet of 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 have a mass m = 1.00×10^-11kg each and leave the nozzle and travel horizontally toward the paper at velocity v = 18.0m/s . The drops pass through a charging unit that gives each drop a positive charge q by causing it to lose some electrons. The drops then pass between parallel deflecting plates of lengthD0 = 2.00cm , where there is a uniform vertical electric field with magnitude E= 7.75×10⁴N/C

1) If a drop is to be deflected a distance d = 0.310mm by the time it reaches the end of the deflection plate, what magnitude of charge q must be given to the drop? Assume that the density of the ink drop is 1000kg/m3 , and ignore the effects of gravity.

q = _______ C

Answer 1

Concepts and reason

The concept used to solve this problem is the charge of the droplet that go through the electric field.

Use the kinematics equation to find the distance of the droplet deflected.

Use the electric force to find the lateral acceleration.

Use the electric field to calculate the charge of the droplet.

Fundamentals

From the kinematic equations,

Expression for the time between the plates is,

Here, t is the time between the plates, L is the length of the plates, and v is the drop velocity.

Expression for the droplet deflection distance is,

Here, d is the droplet deflection distance and a is the lateral acceleration.

Expression for the acceleration in terms of electric force is,

Here, F is the electric force and m is the mass of the droplet.

Expression for the electric force in terms of electric field is,

Expression for the droplet deflection distance is,

Substitute for t.

Rearrange the above equation to get acceleration,

Expression for the acceleration in terms of electric force is,

Substitute for a.

Rearrange to get the electric force,

Expression for the electric force in terms of electric field is,

Substitute for F.

Rearrange the above equation to get the charge of the droplet,

Expression for the charge of the droplet is,

Substitute for m, for v, for d, , and for L.

Ans:

The charge of the droplet is .