Answer:
the required charged is 7.06 × 10⁻¹³ C
Explanation:
Given that;
Radius = 30 microns = 30 × 10⁻⁶
Speed v = 20 m/s
length x = 1.6 cm = 0.016 m
spacing d = 1.0 mm = 0.001 m
Voltage V = 1500 V
from the question, the electric field between the plates is uniform and equal to Voltage divided by the distance between the plates.
Electric field E = V/d
E = 1500 V / 0.001 m
E = 1.5 × 10⁶ V/m
Mass of ink drop m = pv
m = 10³ kg/m³ × [tex]\frac{4}{3}[/tex]πr³
m = 1000 kg/m³ × [tex]\frac{4}{3}[/tex]π × (30 × 10⁻⁶)³
m = 1.131 × 10⁻¹⁰ Kg
Time taken to travel t = x / sped
t = 0.016 m / 20 m/s
t = 0.0008 s
From the kinematic equation
to form the top of a letter 3 mm ( 0.003 m )high
y = [tex]\frac{1}{2}[/tex]at²
2y = at²
a = 2y/t²
we substitute
a = (2 × 0.003 m) / (0.0008 s)²
a = 9375 m/s²
Now Force F = Eq = ma
so
q = ma / E
we substitute
q = ( 1.131 × 10⁻¹⁰ Kg × 9375 m/s² ) / ( 1.5 × 10⁶ V/m )
q = 7.06 × 10⁻¹³ C
Therefore, the required charged is 7.06 × 10⁻¹³ C
