Question

The ink drops have a mass m = 1.00×10−11 kg each and leave the nozzle and travel horizontally toward the paper at velocity v = 20.0 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 = 1.90 cm , where there is a uniform vertical electric field with magnitude E = 7.65×104 N/C .

If a drop is to be deflected a distance d = 0.310 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.

Express your answer numerically in coulombs.

Answer 1

given

mass m = 1.00 X 10⁻¹¹ kg

velocity v = 20.0 m/s

parallel deflecting plates of length D_o = 1.90 cm = 0.019 m

electric field with magnitude E = 7.65 X 10⁴ N/C

deflected a distance d = 0.310 mm = 0.31 X 10^-3 m

density of the ink drop is 1000 kg/m³  

using equation

E = V / d

and

t = D_o / v_x

and we have F = ma

E q = m a

a = E q / m

in y - direction

v_y = 0 + a t

v_y = a t

v_y = ( Eq / m ) ( D_o / v_x )

sameway the displacement is d = 1 / a t²

d = q E D_o² / 2 m v_x²

q = 2 m d v_x² / E D_o²

q = 2 X 1.00 X 10⁻¹¹ X 0.31 X 10^-3 X 20² / 7.65 X 10⁴ X 0.019²

q = 8.9801 X 10^-14 C

the magnitude of charge q must be given to the drop is q = 8.9801 X 10^-14 C