**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 = **p**v

m = 10³ kg/m³ × πr³

m = 1000 kg/m³ × 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 = 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**