# Electrostatics

## Coulomb's Law

\$\$F = k{Q_1⋅Q_2}/{r^2}\$\$

Coulomb's Law states that the force that exists between two charged particles is equal to the product of the two charges, \$Q_1\$ and \$Q_2\$, divided by the square of the distance, r, between them, multiplied by k, Coulomb's constant:

\$\$k = 1/{4πε_0} = 8.99 × 10^9 N m^2 C^{-2}\$\$

where \$ε_0 = 8.55 × 10^{-12} N^{-1} m^{-2} C^2\$, the permittivity of free space.

When a material has a net shortage (positive) or surplus (negative) of electrons in a region, we say that region is charged. Protons and electrons have exactly the same amount of charge, only opposite in sign (polarity). These charges cancel each other out, so in a neutral atom there are exactly the same number of protons as electrons. This is because in the formation of matter as we know it during the Big Bang, all mass particles were created as neutrons. After a fraction of a second, a large proportion of these neutrons split into protons and electrons.

The charge on a proton or electron is called the electronic charge, and its magnitude is \$1.60 × 10^{-19} C\$, where C is the unit of electrical charge, coulomb.

## Conductors

Charge is transferred in solids by the movement of electrons. They move best of all in metals, which have ordered arrays of positive ions surrounded by unattached electrons which can move quickly and easily when a potential is applied across the metal.

Some other non-metallic substances, such as carbon and water, also conduct electricity. Charges may also exist in liquids and gases. A battery has fluid electrolytes, which will carry charged atoms (ions) to electrodes, providing a chemical means of storing electrical energy. Gases may also consist of charged ions.

## Insulators

A polythene rod can be charged by rubbing briefly on material. Notice than electrostatic forces are much stronger than gravity.

Other substances, such as plastic, glass, natural fibres and wood, are insulators. They can accept or lose electrons from their surfaces, but these remain fixed in place and do not move through the material easily.

Insulators may be charged by friction. Rubbing perspex with wool will cause the perspex to become positively charged. Other materials, such as polythene, become negative when rubbed.

Two like charges will repel, and two unlike charges will attract.

## Semi-conductors

There is a third class of materials: semi-conductors. Semi-conductors have limited conductive abilities, and these may change under certain conditions. This provides the means to control conductivity and current direction in an electrical circuit or electronic device. This ability of semi-conductors is exploited in electronics, especially in the silicon chips which make computing possible.

## Induction

A negatively charged insulator, such as a polythene rod, will cause a neutral metallic sphere to polarise. The rod does not touch the sphere, but the presence of a negative electrical charge causes the electrons to be repelled from one side of the sphere.

If the far side of the sphere were now touched by a finger or an earthing wire, the excess electrons would be 'earthed'. This means they would seek to increase their potential energy and leave the sphere, and travel through the conductor to reach the larger neutral mass, the Earth.

When the earth is disconnected, and the rod is taken away, the sphere is left with a net positive charge.

An interesting, and perhaps unexpected, fact is that the net electrical field inside a static conductor is zero. If a charged object is placed inside a hollow container, it will induce a polarisation between the inside and the outside of the container. The degree to which this happens depends on the intensity of the electrical field of the internal charged object. Hence, although there is an induced field outside the container, inside the conductor the electrical fields are opposite and equal in magnitude, so the total net field is zero!

## Electroscope

An electroscope is an instrument which allows an electrostatic charge to be detected and measured. It works by a charge on a top plate causing a vertical rod to be polarised. A gold or aluminium leaf at the bottom of the rod will rise due to repulsion forces in the presence of a net charge.

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