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13 September, 15:15

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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  1. 13 September, 19:05
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    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
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