Ink-Jet Printer Droplet · CAP 2002 #19

Physics · electromagnetism

Problem

In an ink-jet printer, an ink droplet of mass m is given a negative charge q by a computer-controlled charging unit, and then enters at speed v the region between two deflecting parallel plates of length L separated by distance d. All over this region exists a downward electric field which you can assume to be uniform. Neglecting the gravitational force on the droplet, the maximum charge that it can be given so that it will not hit a plate is most closely approximated by [Figure: Shows droplet path between parallel plates with electric field E, length L, separation d, and initial velocity v] (a) mv2EdL2\frac{mv^2E}{dL^2} (b) mv2dEL2\frac{mv^2d}{EL^2} (c) mdE(vL)2\frac{md}{E(vL)^2} (d) m(vL)2Ed\frac{m(vL)^2}{Ed}

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