Lecture 10

Electric and Magnetic Properties of Material

Conductors, Insulators and Semiconductors

The transmission and utilization of electric currents have become an essential ingredient of our modern life. What is an electric current? It is the flow of electric charges in a common direction. In fact, electric currents are measured in
Ampere = Coulomb/second: the current is given by the amount of charge flow per unit time. In the same way, an ocean current is the organized motion of a very large amount of water molecules, and the strength of a current would be measured, e.g., in liters/second.

It follows that, in order to have a current, we must have a substance where charged particles are free to move. We have seen several examples of such substances :

• metals, and other materials containing sizeable amounts of quasi-free electrons
• solutions, that is substances broken up into their constituent ions within the body of a liquid, for example salted water, containing Na⁺ and Cl^- ions. Note that ions are present even in perfectly pure water, since a certain amount of water molecules is broken into H⁺ and OH^- ions
• plasmas, i.e. ionized gases

All of these substances are then capable of transmitting an electric current, and are therefore good electric conductors.

At the opposite end, we find insulators, i.e. materials lacking any amount of free charges and therefore incapable of transmitting a current. In between, there are semiconductors, materials that are neither very good conductors nor perfect insulators.

Even among conductors, there are variations in the ability to carry electric currents. These variations will depend both on the type of material, and on the configuration of the conductor : the same way that a large pipe can carry much more water than a small pipe, a thick copper wire will carry much more current than a thin one.

The human body, given its high contents of fluids, is a rather good conductor (after all the inner functioning of the body is controlled by small electric pulses), while the skin, as long as it is dry, is a reasonably good insulator.

The opposition exerted by a material to the flow of current is called the electrical resistance and its inverse, i.e. the ease of transmitting a current, electrical conductivity. What is the source of resistivity? What impedes, for instance, the flow of electrons within a metal?

As they move along the body of a conductor, electrons collide with the particles of the material they are crossing, and in each collision they transfer some of their energy to the hit molecules. In doing so, the organized motion of the electrons is transformed into random molecular motion:

as a current flows through a conductor, some of the electric energy is dissipated into thermal energy.

We can compare this effect to that of motion in presence of friction : when moving on a frictionless surface, a body in motion would continue moving indefinitely, but the presence of friction gradually transforms the body's kinetic energy into heat.

This transformation of electrical energy into "molecular agitation" might be the desired goal, as in an electric heater or a light bulb. On the other side, it is highly undesireable when the goal is to transmit electrical energy over long distances. In a power line, a large amount of energy is wasted due to resistive losses along the high voltage cables.

For many years, science and technology felt that this was a necessary price to pay, until some new discovery came into the scene.

SUPERCONDUCTIVITY
Note : I will not try to explain, nor I will expect you to know, how superconductivity works. It is enough if you understand what it is and what is its potential importance. You can skip the bottom half of page 358.

Under normal conditions, one can try to minimize the losses due to resistivity, but one cannot eliminate them completely. A completely new phenomenon appears at very low temperatures, typically near the absolute zero.

Reminder from Phys 101 : theory and experiment have shown that there is a limit on how low a temperature a body can have. Such a limit is called absolute zero and it corresponds to $\sim$-273 degrees centigrades. Absolute temperatures are measured in Kelvins : 0 K = absolute zero = -273⁰ C

It was oserved in 1911 (and the theoretical model to explain the phenomenon did not arrive until the '50s) that many conductors, when kept below a temperature of a few Kelvins, exhibit completely different electrical properties and are capable of carrying a current without any resistive losses ; this effect was called superconductivity.

This behaviour opens up an incredible amount of potential applications. As an example, once a current is established (e.g. with a battery) in a superconductive circuit, the current will keep flowing even if the battery is removed.

Thanks to superconductivity, one can run very high currents, that, in the normal conductivity regime, would be impossible to reach since they would overheat and melt the conductor. The potential of such a phenomenon for practical applications is in principle very large, but there are some difficulties:

TECHNICAL QUESTION : how can one keep a circuit at a temperature near absolute zero?
ANSWER : keep it immersed in a bath of liquid Helium (Helium boiling point = 4 K). This is in principle feasible, but it is neither practical nor economical , since it takes a fair amount of machinery to produce liquid Helium. To date, superconductivity has seen applications in limited fields, -high energy particle accelerators, medical Magnetic Resonance Imaging- where very high magnetic fields are required, and where the substantial equipment required to liquefy Helium can be afforded.

Very recently (1986) a major breakthrough has occurred : two Swiss researchers found a new class of ceramic-like materials (therefore unlikely candidates for being conductors) that exhibit superconductivity at much higher temperatures , as high as 160 K. These "High Temperature Superconductors" have already passed an important threshold, represented by the boiling point of Nitrogen, i.e. 77 K. Given that it is much more easy and economical to produce liquid Nitrogen than liquid Helium, the field of High Temperature Superconductivity has the potential for a vast array of very interesting applications. Still, it might take a few decades before we see its widespread utilization.

MAGNETIC PROPERTIES of MATERIALS

We have just said that high (superconducting) currents can be used to generate strong magnetic fields, this is then a good moment to re-examine magnetism, and understand its origins at the atomic level.

Question: which of the following statements is not true? (you can give more than one answer if you believe there is more than one untruth)

A an electric charge at rest generates a magnetic field

B an electric charge at rest is affected by a magnetic field

C a moving charge generates a magnetic field

D a moving charge is affected by a magnetic field

E an electric current generates a magnetic field

F an electric current is affected by a magnetic field

It is then a fact that magnetic fields are generated by charges in motion. In fact, as we will now realize, all magnetic fields are due to charge motion.

Thinking of the structure of matter at the atomic level, we can see that an electron orbiting around the nucleus is behaving like a microscopic current loop. Any orbiting electron will therefore generate a tiny magnetic field. Each atomic electron behaves like a mini-magnet, but, in general, all of the individual magnetic fields associated with each electron will be oriented randomly, therefore no net magnetic field is observed.

On the other side, there is a class of materials that behaves differently : in several iron-like metals (Iron, Nickel, Cobalt), atoms have the capability of organizing themselves into groups (called magnetic domains) with the same orientation of the field within a group. Moreover, when immersed in a strong enough magnetic fields, all of the domains can rearrange themselves in the direction of the field, and this will cause the whole material to behave like a magnet (and therefore to be attracted by a magnet). Turning off the field, the iron will soon return to its original state of randomly oriented domains.

Finally, in some even more special case, all of the domains are frozen in an aligned status (this can happen when a melted metal is gradually cooled down in the presence of a strong magnetic field). In this case the magnetization of the material is permanent, we are then dealing with the familiar permanent magnets.