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 \(\texttip{m}{m}\) = 1.00

Answer 1

The force, F, experienced by a particle with charge q in a uniform electric field of magniqude E (the type of field between the charged plates in this question) is:

F = q*E

By Newton's second law, F = m*a, so if the particle has mass m, it will undergo a constant acceleration of:

a = q*E/m

The equation of motion for a particle undergoing constant acceleration is:

delta-y = 0.5*a*t^2 = (q*E/(2*m))*t^2

(2*m*delta-y)/(E*t^2) = q

where delta-y is the change in position at time t, from the starting position.

There are no forces acting on the droplet in the direction of its initial velocity (parallel to the plates), so the droplet's velocity parallel to the plates is constant. That means it will take:

t = 2.2cm/(21 m/s) = 10.4*10^-4 sec

for the droplet to traverse the plates. This is the amount of time that the droplet is subjected to the transverse acceleration, so:

2*(1.00*10^-11 kg)*(3.1*10^-4 m)/((8.45*10^4 N/C)*(10.4*10^-4 sec)^2) = q

8.02*10^-19 C = q