Electricity

If you drag your feet on a carpet in dry weather you will acquire a static charge. You can discharge on the nearest brass door-knob. Amber rubbed with fur acquires a static charge. A glass rod rubbed with silken cloth acquires a different kind of charge. All these effects are due to the transfer of electrons from one object to another. The object with excess electrons is called negative. The object that lost the electrons is called positive.

If like-charged objects (both negative or both positive) are brought near each other there is a repulsive force between them. Opposite charged objects attract each other. In both cases the resultant force increases as the objects are brought near each other. This force is proportional to the product of the two charges and is inversely proportional to the square of the distance between them. This is known as Coulomb’s law.

The q₁ and q₂ represent the charges. The r represents the distance between what are regarded as point charges. For two like-charged particles to be brought together from infinite separation, a certain amount of work against the repulsive force is required. This stored energy is called potential energy. If the force bringing the particles together is removed they will fly apart. The potential energy is converted to kinetic energy. Similarly, work is required to move opposite charged particles away from each other. Work is done against a force over a distance (work = force x distance). Thus the potential energy is expressed as the product of the two charges divided by the distance between the particles.

Electric current is the flow of charged particles. This is most commonly found in metallic conductors. In the case of metals electrons move through a rather rigid lattice of metal ions. Metals are characterized by loosely held electrons. In a metal, the electrons are not associated with particular metal ions. They are similar to a gaseous cloud. They move through the lattice structure under the slightest impulse. This force is called a potential gradient or electric field.

In an electric field, an electron experiences a constantly applied force. Yet it doesn’t continue to accelerate. This is due to frequent collisions with the lattice structure that slow it down. An equilibrium is reached which results in an average velocity and thus a constant current.

The charge on an electron is -1.602 x 10^-19 coulombs. The charge on a proton is the same magnitude and opposite sign. An ampere (A) is a measure of current. The passage of one coulomb (C) per second across a section of a conductor is a current of one ampere. Thus a coulomb is an amp second. (C = A s). A potential difference is measured in volts. An electric field is measured in volts per distance. The resistance R to the movement of charge in a potential gradient is related to current I by Ohm’s law.

Given a potential difference between two points, the field strength depends on the distance between the two points; the further apart they are the smaller the field strength. It would seem that under these conditions there would be less current for a given potential difference and indeed it does. Thus R is not a constant for a given material and depends on the distance through which the current is passed. The resistivity of a material, independent of size and shape, is represented by r. The resistance of a sample of a material is proportional to the resistivity r and the length l along which the current flows and is inversely proportional to the cross-sectional area A of the sample.

Metals, in general, have a low resistance to the flow of current. The resistance increases with increased temperature. This is due to increased movement of the lattice and a greater frequency of collisions between the moving electrons and the lattice.

Some solids are very poor conductors of electrons. In these substances (insulators) the electrons are tightly bound to the nuclei. Semiconductors have an energy gap between the bonding electrons and the conduction band. They do not conduct at the slightest potential difference but require a certain minimum field strength in order to overcome the energy gap between the valence band and the conduction band. Electrons promoted to the higher energy conduction band cause the semiconductor to conduct a current. The promotion of electrons into the conduction band leaves "holes" in the valence band. Electrons move in one direction while the positive holes move in the opposite direction. In this case conduction is enhanced by an increase in temperature.

Conduction in an electrolyte solution is similar to conduction in a semiconductor in that the current is carried in one direction by negative particles and in the other direction by positive particles. In the case of an electrolyte the charged particles are ions. Positive ions are called cations. Negative ions are called anions. A typical cation is K⁺. A typical anion is Cl^-. A polar solvent is required. The most common solvent for an electrolyte solution is water.

Current can be carried by ionized gases as in fluorescent bulbs. Some unusual solids can conduct cations through a lattice of anions. Ice can conduct protons and silver chloride can conduct silver ions at elevated temperatures. Molten salts conduct by movement of both anions and cations.