A grain of dust with a mass of m = 10pg having a charge q = 4 * 10 ^ -14kl are in equilibrium

A grain of dust with a mass of m = 10pg having a charge q = 4 * 10 ^ -14kl are in equilibrium between 2 parallel plates located horizontally, the distance between the plates d = 5cm is to find the voltage between the plates.

m = 10 pg = 10 * 10 ^ -12 kg.

g = 9.8 m / s ^ 2.

q = 4 * 10 ^ -14 Cl.

d = 5 cm = 0.05 m.

U -?

Two forces act on a speck of dust: the force of gravity m * g and the electrostatic force of the electric field F.

Since a speck of dust is at rest, then, according to Newton’s 1 law, these forces cancel each other out.

F = m * g.

Let us find the electrostatic force by the formula: F = q * E, where q is the charge of the dust grain, E is the electric field strength.

E = U / d.

q * U / d = m * g.

U = d * m * g / q.

U = 0.05 m * 10 * 10 ^ -12 kg * 9.8 m / s ^ 2/4 * 10 ^ -14 Cl = 122.5 V.

Answer: the voltage between the plates is U = 122.5 V.