If a drop is to be deflected a distance d = 0.350 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.

Question

Physics

Janessa Preston

30 April, 12:23

If a drop is to be deflected a distance d = 0.350 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.

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Answers (1)

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Taylor Buckley · Answer 1

q = 4.87 X 10^ - 14 C

Explanation:

As d=0.350 mm

The ink drop will be accelerated by the electric field between the plates:

a = F/m

d = a (D0 / v) ^2 / 2 ... 1

a = qE/m ... 2

Substituting 2 into 1:

d = (qE/m) (D0 / v) ^2 / 2

q = 2mdv^2 / [E (D0) ^2]

q = 2 (1.00e-11 kg) (3.50e-4 m) (15.0 m/s) ^2 / [ (7.70e4 N/C) (2.05e-2 m) ^2]

q = 4.87e-14 C