A grain of dust with a mass of 10⁻⁸ g, having a charge of 1.6 * 10 ⁻¹⁷ C, is in a uniform electric field.

A grain of dust with a mass of 10⁻⁸ g, having a charge of 1.6 * 10 ⁻¹⁷ C, is in a uniform electric field. Determine the field strength if the gravity of a dust particle is balanced by the action of an electric field on it.

To find out the required field strength, consider the equality: mp * g = Ex * qp, from where we express: Ex = mp * g / qp.

Const: g – acceleration due to gravity (g ≈ 9.8 m / s2).

Data: mp is the mass of the specified dust grain (mp = 10 ^ -8 g; in the SI system mp = 10 ^ -11 kg); qp is the charge of the dust grain (qp = 1.6 * 10 ^ -17 C).

Let’s perform the calculation: Ex = mp * g / qp = 10 ^ -11 * 9.8 / (1.6 * 10 ^ -17) = 6.125 * 10 ^ 6 V / m = 6.125 MV / m.

Answer: The required field strength is 6.125 MV / m.