# An electric field problem

#### Kudo Shinichi

1. Homework Statement
An ink-jet printer uses drops of ink which have a radius of r=3.0x10^-5 m and a density equal to that of water (1.0 x ^3 kg-m^-3). The drops are ejected horizontally from a nozzle with a speed Vo=18m/s, as shown in the figure. The drops pass through electrostatic deflecting plates which are separated by d=2.0mm and have a length of L=1.0cm. The potential difference between the plates is 3000V. Paper is positioned a distance L from the ends of the plates.
http://tinypic.com/view.php?pic=15kppf&s=5
a)Neglecting gravity, air resistance and fringing fields, determine the range of values of the charge q on the drops required to write a character 2mm high centered on the axis of the nozzle.
b)Estimate the deflection if gravity acted alone over the flight path of 2.0cm. Is gravity important?
c)Estimate the maximum deflection caused by the earth’s magnetic field. Assume the magnetic field B is oriented horizontally and perpendicular to the velocity and has a magnitude of 6.0x10^-5 T. Is the earth’s magnetic field important?

3. The Attempt at a Solution
a)First of all, I tried to figure out what F is.
v=potential/(magnetic field x distance between plates)
magnetic field= 3000V/(18 x 2x10^-3)=8.33 x 10^-4
density=current/(charge of electron x velocity x area)
since all the values except current are given, so just plug in and solve for current
current=1.152 x 10^-19
use F=I x l x B to solve for force and the force is 1.92 x 10^-16
then use F=q x v x B to solve for charge which is 1.28 x 10^-22
However, the answer I got is not a range of charge
I don't really know how to do part b and c, can I use the force I got from part a in these two parts? or is there any other ways to solve the problem?

Any comment or help would be great. Thank you very much.

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