# Can dust particles be charged electronically

### Particle adhesion due to static electricity

When particles move in currents of air caused by air conditioners or similar devices, they take on a positive or negative charge through contact with various objects. Positively charged particles are attracted to negatively charged objects and vice versa. The more particles there are in the air, the more particles adhere to the objects in the room. If the particle sources (usually people and clothing) are also electrically charged, the particles emanating from these sources are also electrically charged. This attractive force generated by electrostatic charges is known as the Coulomb force.
The Coulomb force is expressed using the following formula:

F 3338 is the Coulomb force, Q1 and Q2 [C] are electrostatic charges, d [m] is the distance between the charges and ε0 [F / m] is the electrical constant (ε0 = 8.85 × 10-12 F / m). The greater the electrostatic charge of the objects, the greater the Coulomb force and the weaker the greater the distance between the objects. If the distance is multiplied by 2, the Coulomb force is 1/4 of its previous value. If the distance is multiplied by 10, the Coulomb force has 1/100 of its previous value. This means that the force acting between two objects with a distance of 1 mm is reduced to 1/100 of its previous strength when the distance between the objects increases to 10 mm.

### Attachment of particles to particles

We have calculated the distance at which two highly charged objects begin to adhere to one another due to the Coulomb force.

The distance is shown on the horizontal axis and the Coulomb force on the vertical axis. The three lines indicate three examples with different particle sizes. The three different particles have a diameter of 0.5 μm, 5 μm and 50 μm. Let us concentrate on points A, B and C. They mark the distances at which the Coulomb force acting between the particles and the gravitation acting on the particles are in equilibrium. This means that the particles stick to each other when the distance between them decreases because the Coulomb force is greater than gravity. If the distance is greater than indicated by the dots, gravity exceeds the Coulomb force and the particles fall to the ground without sticking to each other. The 5 μm particles attract each other at a distance of less than 0.1 mm. If the distance is 0.1 mm or more, the particles fall to the ground without sticking to each other. It follows that particles only adhere to one another as a result of electrostatic charging if the distance between them is extremely small.

### Attachment of particles to objects

The size of the Coulomb force also changes with the strength of the electrostatic charge. In other words, the size of the Coulomb force depends on what kind of object is electrostatically charged. Since particles are only weakly electrostatically charged, they only adhere to one another if they are very close. Let's look at the case where both a particle and an object are electrostatically charged. Since the object is significantly larger than a particle, the amount of static electricity is greater. It is also true that the attenuation of the Coulomb force in a large object is no longer inversely proportional to the square of the distance. We left out the detailed calculations, but if the object is electrostatically charged, it can attract particles from a distance of 20, 30 and more centimeters.

Next, let's look at the case where the object is not electrostatically charged, but the particles are. In this case, there is another aspect to consider: the conductivity of the object. First, let's consider a ladder. When electrostatically charged particles approach the conductor, static electricity is generated on the surface of the conductor, which is opposite to the charge on the particles. The reason for this is the movement of the electrical charges in the conductor. This phenomenon is known as electrostatic induction.

Grounding the object is ineffective as a countermeasure for this phenomenon. This does not prevent an opposite charge from building up as a result of the Coulomb force. The only possible countermeasure is the electrostatic discharge of the particles. Since the electrostatic charges of a conductor and the particles are opposite to each other, the Coulomb force occurs.
As before, we calculated the distance at which a particle is attracted to an object.

For particles with a diameter of 5 μm, the Coulomb force becomes so great that a particle adheres to the object at a distance of 0.1 mm or less. Particles do not adhere to the object if the distance between the two is at least a few millimeters.
However, only the particles are electrostatically charged and the charge is small, so that the Coulomb force is weak and the distance at which the particles adhere to the object is only a few millimeters.

Next, let's look at the case where the object is an uncharged insulator and only the particles have an electrostatic charge. Non-conductors have an insulating effect on electricity. Therefore there is no electrostatic induction. In the above formula for the Coulomb force, since the charge Q1 is zero, the Coulomb force is also zero. In other words, the particle does not adhere to the object.