In an inkjet printer, letters are built up by squirting drops of ink at the pape

Question

In an inkjet printer, letters are built up by squirting drops of ink at the paper from a rapidly moving nozzle. The ink drops, which have a mass of 1.3 times 10^-8 g each, leave the nozzle and travel toward the paper at 21 m/s, passing through a charging unit that gives each drop a positive charge q by removing some electrons from it. The drops then pass between parallel deflecting plates 2.0 cm long where there is a uniform vertical electric field with magnitude 7.9 times 10^4 N/C. If a drop is to be deflected 0.31 mm by the time it reaches the end of the deflection plates, what magnitude of charge must be given to the drop?

Explanation / Answer

time taken , t = 0.02/21

                      = 9.524 * 10-4 sec

Here, 0.31 * 10-3 = 1/2 * a * ( 9.524 * 10-4)2

=> a = 683.52 m/s2

As, qE = ma

=> q * 7.9 * 104 = 1.3 * 10-8 * 10-3 * 683.52

=> q = 1.1247 * 10-13 C

Thus, magnitude of charge given to drop =   1.1247 * 10-13 C

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