The ink drops have a mass m = 1.00×10 11 kg each and leave the nozzle and travel

Question

The ink drops have a mass m = 1.00×1011 kg each and leave the nozzle and travel horizontally toward the paper at velocity v = 25.0 m/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 length D0 = 2.00 cm , where there is a uniform vertical electric field with magnitude E = 7.55×104 N/C

1. If a drop is to be deflected a distance d = 0.250 mm 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 1000 kg/m3 , and ignore the effects of gravity.

Explanation / Answer

Here ,

initial velocity , v0 = 25 m/s

time taken for the drops to travel , t = distance/speed ,

t = 0.02/25 s = 0.0008 s

Now , for delflection , d = 0.250 mm

let the acceleration of the drop is a

Using second equation of motion

d = 0.5 * a * t^2

0.250 * 10^-3 = 0.5 * a * (0.0008)^2

a = 781.3 m/s^2

let the charge is q

q * E = m *a

q * 7.55 *10^4 = 1 *10^-11 * 781.3

q = 1.034 *10^-13 C

the charge q on the ink is 1.034 *10^-13 C

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