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 = 1.50 cm , where there is a uniform vertical electric field with magnitude E = 8.40×104 N/C If a drop is to be deflected a distance d = 0.270 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

velocity along x direxction vx should be constant since there is no force along x axis

vx = 25.0 m/s

The time electron travled inside the capacitor is t

t= S/vx     (S is distance traveled in x direction)

t= 0.015/25 = 6*10^-4 s

distance travelled in y direction

y= -0.00027 m

F= Eq

E= ma/q

y=0+at2/2

a= 0.00027*2/t2 = 1500 m/s2

m=1* 10^-11 kg

E= 8.4 *10^4 N/C

q=ma/E

q=1* 10^-11 *1500/ 8.4 *10^4 = 1.7857 *10^-13 C

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