The strength of the Earth’s electric field is 121 V / m and is directed vertically downward.

The strength of the Earth’s electric field is 121 V / m and is directed vertically downward. What is the acceleration of a dust particle weighing 27 micrograms carrying a positive charge of 649 pC? Disregard air resistance.

E = 121 V / m.

m = 27 μg = 27 * 10 ^ -9 kg.

g = 9.8 m / s2.

q = 649 pC = 649 * 10 ^ -12 C.

a -?

Two forces will act on a speck of dust: gravity Ft directed vertically downward and electrostatic force Fe, which is also directed downward.

2 Newton’s law will have the form: m * a = Ft + Fe.

The force of gravity Ft and the electrostatic force Fe are determined by the formulas: Ft = m * g and Fe = q * E.

m * a = m * g + q * E.

The acceleration of a grain of dust will be determined by the formula: a = g + q * E / m.

a = 9.8 m / s2 + 649 * 10 ^ -12 C * 121 V / m / 27 * 10 ^ -9 kg = 12.7 m / s2.

Answer: a grain of dust will move with acceleration a = 12.7 m / s2.