The ink drops have a mass m = 1.00×1011 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 = 1.65 cm , where there is a uniform vertical electric field with magnitude E = 7.80×104 N/C . If a drop is to be deflected a distance d = 0.320 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

motion parallel to plates:
D0 = (v)(t)
t = D0 / v ........................[1]

motion perpendicular to plates:
d = at^2/2 ........................[2]

Substitute [1] into [2]:
d = a(D0 / v)^2 / 2 .....................[3]

The ink drop will be accelerated by the electric field between the plates:
a = F/m
a = qE/m .........................[4]

Substituting [4] into [3]:
d = (qE/m)(D0 / v)^2 / 2
q = 2mdv^2 / [E(D0)^2]

q = 2(1.00e-11 kg)(3.20e-4 m)(25.0 m/s)^2 / [(7.80e4 N/C)(1.65e-2 m)^2]
q = 1.88 e-13 C

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