Chapter Seven Electricity and magnetism
Knowledge of electricity and magnetism has been with us for centuries: the Greeks knew that, if you rubbed amber against fur, you could generate static electricity; indeed, their word for amber, ‘elektron’, was the word used by the 16th century physicist, William Gilbert, to describe the way in which amber and other objects capable of becoming electrostatically charged could attract and repel other objects. This, in turn, gave rise to the English words ‘electric’ and ‘electricity’.
Gilbert, who published his ideas in 1600, three years before his death at the age of 63, in the work De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (‘On the Magnet, Magnetic Bodies, and the Great Magnet of the Earth’), was also the first person to suggest that electricity and magnetism might be different manifestations of the same fundamental force. Magnetism had also been known to the ancient Greeks; its first practical application was the navigational compass, but it would not be until the 19th century that the laws of electricity and magnetism would be quantified and unified.
Until 1800, when Alessandro Volta succeeded in making a battery using plates of zinc and silver interspersed with damp cardboard, the study of electricity had been confined to electrostatics, the physics of static charges. Pioneering physicists such as Priestly, Coulomb, Poisson and Faraday had succeeded in showing that both static electricity and magnetism followed the same inverse square law as gravity; in this case known as Coulomb’s Law.
Volta had actually made his name by discovering and isolating the gas methane. It was his friendship with Luigi Galvani – famous for the ‘Galvanic effect’ of contracting the muscles of (dead) frogs by the application of copper and silver plates – that kindled his interest in the subject of electricity. The battery was subsequently developed almost by accident; because of the serendipitous happenstance, the volt was named after him.
You will recall that Coulomb’s Law was defined in the previous chapter: the electric force between two charged masses is proportional to the size of the two charges and inversely proportional to the square of the distance between them.
Despite its attribution to Coulomb, this relationship was actually first described by Joseph Priestly; proved quantitatively by Henry Cavendish and John Robinson, neither of whom bothered to publish their work; and confirmed experimentally by Michael Faraday. Such are the vagaries of eponymic immortality in the world of physics.
Electricity remained a scientific oddity until the development of the wire telegraph in the late 1830s, which started the revolution in communication – suddenly, it was possible to send messages across continents in minutes rather than weeks.
The invention of the telegraph, and the code which it utilized for its messages, is commonly credited to Samuel Morse. In fact, William Cooke and Charles Wheatstone patented and built the first telegraph in 1836 on a stretch of the Great Western Railway in England fully 8 years before Morse (who was actually an artist rather than an inventor or scientist) – even the code of dots and dashes was developed in the main by his business partner, Alfred Vail.
Despite the increasing practical applications of electricity, its true nature remained a mystery for another 30 years when the Scottish physicist James Clerk Maxwell described the first element of the ‘Holy Grail’ of physics, the Unified Field Theory, when he successfully demonstrated that electricity and magnetism were merely different manifestations of the same fundamental force.
Although the two forces seem quite distinct on a mundane level, and are governed by different equations, it is a remarkable fact that a changing electric field will create a magnetic field and, conversely, a changing magnetic field will generate an electric field – the principle on which the dynamo that powers bicycle lights works.
The theory that, in particle physics, all fundamental forces and the relationships between the elementary particles can be described with a single theoretical framework. Electricity, magnetism and the weak nuclear force have been successfully unified and the theory has been established to add the strong nuclear force, though experimental evidence is beyond the capabilities of current particle accelerators. The extremely weak, long-range force of gravity remains beyond attempts to bring it within the fold.
This relationship between electrical and magnetic fields has an important implication for the physician. We have seen in previous chapters that many of the particles that comprise the human body have a charge associated with them and that certain particles, including protons, have spin.
As protons have a positive charge and are spinning, this means they must also have a magnetic field associated with them: effectively a ‘north pole’ and a ‘south pole’, just like a miniature Earth, which, in turn, has a magnetic field generated by its spinning iron core. By contrast, the moon – which has no such core and is no longer spinning – has no magnetic field.
This means that, if you were to put them in a strong magnetic field, the protons’ magnetic fields would all line up the same way. When the field is switched off, the protons would revert to their original state, emitting photons as they do. All you would need to do is set up a ring of photon detectors and you could build up an accurate three-dimensional picture of the concentrations of protons in the sample being imaged.
Fortunately, the body is replete with free protons – hydrogen ions. Indeed, with its ubiquitous presence in organic and water molecules, hydrogen is easily the most common atom (and ion) found in our bodies and the principle that has just been described is that behind the working of an MRI (magnetic resonance imaging) machine (of which more in Chapter 9).
Maxwell also showed that electric and magnetic fields travel together through space as waves of electromagnetic radiation, with the changing fields mutually sustaining each other. Examples of such waves are radio and television signals, microwaves, infrared rays, visible light, ultraviolet light, x-rays, and gamma rays. In Maxwell’s time, all waves were thought to need a medium to propagate them and, in the absence of any tangible medium to support light and radio waves (which could obviously travel in the vacuum of space), the ‘ether’ was proposed as the intangible medium of propagation. It was Maxwell who showed that electromagnetic waves required no medium.
All of these waves travel at the same speed, the velocity of light (roughly 3 × 108 ms−1). They differ from each other only in the frequency at which their electric and magnetic fields oscillate; prior to Maxwell, many of these phenomena (or those that had by then been discovered) were regarded as being unrelated.
The study of non-moving electrical charges now forms such a small part of the study of electricity as a whole that it is hard sometimes to remember that, for many centuries, it was the only form of electricity that could be studied. It was, however, a necessary step to understanding electrical phenomena as a whole and, as we have seen, has critical implications for the shape and function of many organic molecules.
here Q1 and Q2 are the size of the respective charges and d is their separation.
Today, we take for granted electricity in every aspect of our daily – and clinical – lives: light at the flick of a switch, computerized patient records, electromagnetic treatment modalities, diagnostic imaging, electrically powered treatment benches, digital thermometers, ophthalmoscopes, dictaphones, air-conditioned and heated offices – the list could continue for pages; electricity is so much a part of our lives that we only appreciate it when a power cut robs us of access.
One hundred-and-fifty years ago, physicians had no such luxuries. I have, in the corner of my consulting room, a reminder that for our predecessors even something as simple as getting sufficient illumination to make an adequate examination could be a major challenge. The doctor’s double oil lamp (Fig. 7.1), came with two lamps, each with a double burner, mounted on pivoted arms so the full force of the light could, when required, be brought to bear on the patient. I have tried the lamp – it produced, I would estimate, the equivalent of a 5 watt bulb and had the added disadvantage of setting off the (electric) fire alarms.
At the time it was made, around 1860, neither chiropractic nor osteopathy existed and the term ‘physiotherapy’ had yet to be coined. Physicians still used leeches and surgical anaesthesia was in its infancy; manual therapy was in the hands of bonesetters.
Interestingly, the founder of chiropractic, Daniel Palmer, originally plied his trade as a ‘magnetic healer’ in the American mid-west of the 1890s. Over a century later, what has been sneered at as evidence of the ‘quack’ origins of the profession he began is now under serious investigation as a noninvasive therapy for a range of musculoskeletal and vascular conditions with proven physiological effects on the numerous polar molecules within the human body.
You will (hopefully) recall from Chapter 2 that potential energy is energy that has been stored. A system with potential energy has the capacity to do work when the stored energy is released. A convenient source of this potential energy is the battery or electric cell (Fig. 7.2).
Figure 7.2 • ‘Dry-cell’ battery, so-called to differentiate it from the early voltaic piles that employed plates of zinc and either silver or, for economic reasons, copper interspersed with wet paper to provide a medium conducive to electrolysis.
One way of thinking about a battery is that it contains lots of electrons that have been packed close together. Because ‘like’ charges repel, these negatively charged electrons have potential energy because they do work as soon as they fly apart. If these electrons are put at one end of an electric cable, this repulsive force will cause some of the electrons to move along the wire and work can be done. The more the electrons are packed together, the greater the repulsive force and the greater the electric potential, commonly called the voltage, V, because volts are the unit used to measure electric potential. The volt (V) is the potential energy per unit charge (in this case, the electron) and is equivalent to the number of joules per coulomb. The electric potential can be measured using a voltmeter.
Although it is tempting to think of the material world as being divided into two – those substances that do conduct electricity and those (insulators) that do not – the true picture is more complex by far. We have talked about connecting an electric potential to an electric cable in order to obtain a current but the results we get will be very different, depending on the material from which the cable is made.
There are actually not two but four classes of conductive substance. The first group comprises superconductors. Early in the 20th century, physicists discovered that when certain metals are cooled below their transition temperatures (typically less than 20 K), they lose all resistance to electron flow. This means that a current can flow indefinitely without any electrical potential to drive it – it was, and remains, the closest thing to perpetual motion; imagine having a car that, once started, would continue without ever decelerating (the catch, of course, is the amount of energy required to cool to and maintain a temperature of 20 K).
In the 1980s, a breakthrough occurred when it was found that certain ceramic compound materials which, at normal temperatures are extremely poor conductors of electricity, when cooled sufficiently would also act as superconductors. Unfortunately, nobody knows why, which makes the search for high-temperature superconductors a matter of trial and error with increasingly complicated ‘designer’ molecules.
By 1986, a molecule comprising yttrium, barium, copper and oxygen was exhibiting superconductivity at temperatures of 92 K, above the liquification point of nitrogen. The current record of 138 K is held by a thallium-doped, mercuric-cuprate consisting of the elements mercury, thallium, barium, calcium, copper and oxygen, although recent claims have been made for a lead-doped composite of tin, indium and thulium, which has been reportedly observed superconducting at 181 K, only −92°C. By comparison, the lowest climatic temperature ever recorded is −89.2°C at Vostok in Antarctica in July 1983.
Conventional electrical conductors are those materials that allow the easy transmission of an electrical current. Most conductors are metals and the charge carriers are the outer electrons of the individual atoms, which can move about the atomic lattice formed by the metal without ‘belonging’ to any one atom. These free-moving, conductive electrons are sometimes referred to as the ‘electron gas’. Ionized gases and electrolytic solutions can also act as conductors; here, the charge carriers are ions.
Typically, electric cables are made from copper or aluminium; however, unlike superconductors, these metals do not conduct perfectly – there is resistance (R) to the electron flow. Using the previous analogy to our perpetually moving car, in the real world the car is slowed by the resistance of the air molecules through which it must move.
Electrical resistance is measured in ohms (Ω). Typically, copper wire offers a resistance of 0.15 Ω per metre length, although this will depend, amongst other things, on the thickness of the wire. Because of these variable factors, a material will be referred to in terms of its resistivity (ρ), calculated by taking the resistance of the wire, multiplied by its cross-sectional area and divided by its length. Conversely, conductance, G, is measured in siemens (S) or, occasionally, the ‘mho’ (‘Ohm’ spelt backwards).
The man after whom the unit of resistance is named, Georg Simon Ohm, was the first to experimentally observe the relationship between voltage, current and resistance. This law states that, for a conductor, the amount of current flowing in a material is directly proportional to the potential difference across the material. The constant of proportionality is the resistance. Thus:
Graphically, this can be demonstrated by plotting current against voltage (Fig. 7.3).
Materials that do not readily conduct electricity are termed insulators. In reality, they may be regarded as being at the opposite end of a spectrum that starts with superconductors: insulators are in fact merely conductors with extremely high resistivity. Typical examples of such materials are glass, rubber and the plastics that coat electrical cables so that they may be handled without the inadvertent transfer of electricity to the electrician – the classic electric shock! With insulators, the outer electrons are tightly bound to the atoms and are therefore not available to carry charge: the higher the binding energy, the better the insulator.
Halfway down our spectrum of conductivity lie materials that have both conductive and insulating capabilities. Therein lies the field of solid state physics, a subject whose scope and complexity lie well beyond the limitations of this text; however, this branch of physics underpins the working of nearly every electronic device: computers, mobile phones, televisions, radios, MP3 players and, increasingly, domestic appliances. Anything with a ‘chip’ or transistor is reliant upon the atomic and molecular properties of semiconductors and it is therefore worth understanding the basic principles behind semi-conductors.
In intrinsic semiconductors, such as germanium and silicon, the outer electrons, which are loosely bound, form covalent bonds with neighbouring atoms. They can, therefore, be released quite easily if energy is imparted to the system by increasing its temperature. A free electron will leave behind it a ‘hole’, which may then be filled by another free electron. This ‘hole’ will therefore move from electron to electron, in effect becoming a positive charge carrier. This arrangement is known as a hole–electron pair.
In an extrinsic semiconductor, small traces of impurities are deliberately added in a process known as ‘doping’. If the impurity is from Group III of the periodic table, such as indium or gallium, when it joins with the semiconductor material there will only be three electrons free to fill four valence bonds (silicon and gallium are both from Group IV). An electron is therefore ‘borrowed’ from a neighbouring Group IV atom, creating a ‘hole’ in the same way that a non-doped sample works, albeit more efficiently. This type of extrinsic semiconductor is known as a p-type semiconductor.
By contrast, an n-type semiconductor is obtained when Group V impurities, such as antimony or arsenic, are added. Once the four valence bonds required by silicon or germanium are satisfied, there is an electron left over, which can then act as a charge carrier. In n-type semiconductors, conduction is therefore mainly due to free electrons, although intrinsic ‘holes’ will also still carry positive charge in the opposite direction.
By sandwiching together layers of p-type and n-type semiconductor material, the transistor was invented to replace the large, cumbersome and unreliable valve components of electronic circuits prior to the 1960s. No longer did radios – which could suddenly fit in your pocket – take half a minute to ‘warm up’. Finally, it was possible to build a computer that didn’t require a room the size of a house to contain it and wouldn’t require a component replacement every few hours.
Within a generation, the transistor was replaced by the integrated circuit, which itself became miniaturized, with p-n-p or n-p-n junctions of atomic widths now appearing in the microchips that allow our radios to store thousands of MP3s whilst fitting in our credit card holders, and our computers to fit into hand luggage. A single, modern chip can contain millions of components packed in to a few square millimetres.
The study of moving charges is known as electrodynamics. For our purposes, this will comprise a study of the way in which electricity and electrical components work. This will enable us to understand the operation of such devices as we encounter and rely on in our clinical practice. Clinical tools such as the ophthalmoscope; diagnostic imaging of all types, be it ultrasound, magnetic resonance imaging, conventional x-rays or cutting edge proton emission tomography; and therapeutic interventions such as interferential or TENS machines all rely upon one common factor, the flow of electricity.
This flow of electricity through a conductive device or apparatus can be best described using a circuit diagram. This is the electrical equivalent of a map and, like a map, it utilizes symbols to describe the topography through which the electricity flows. The most common symbols – and certainly all those you are likely to encounter in the course of your studies and subsequent clinical career – are detailed in Figure 7.4.
The direction in which electric current flows is important; unfortunately, early physicists assumed that positive charges were moving when electricity flowed and so, on a circuit diagram, the current moves from positive to negative. This is known as conventional current but takes place in the opposite direction to actual electron flow; electrons are of course attracted towards the positive terminal and repelled by the negative. Conventional current is used by electricians and electron flow by physicists. The circuit diagrams you encounter in this book, and most others that you (as clinicians) are likely to read, will be based on conventional current.
In order for a current to flow, there must be a continuous circuit running out from and back to the source of the electric potential: electrons will then flow down the potential gradient (Fig. 7.5). If there is a break in the circuit then no current will flow (this is how a switch works). Current flow can also be disrupted by a short circuit (where two wires within the circuit touch in such a way that the continuous flow of electrons is broken).
Figure 7.5 • In order for a current to flow, there must be a continuous circuit between the two terminals of a battery (B). If there is a break in the circuit (such as that provided by an open switch), no current can flow (A). The same effect is achieved if there is a ‘short’ in the circuit (C).
The type of current provided by a battery gives a continuous flow of electrons (Fig. 7.6A), at least until the battery becomes ‘flat’ when its charge is exhausted. Unfortunately, this direct current is limited in its ability to be generated and transmitted over long distances, which is why domestic electricity comes in a different form, known as alternating current (Fig. 7.6B).
Figure 7.6 • With direct current, there is a steady, unbroken flow of electrons (A). With alternating current (B), the current first flows in one direction AB reaching a maximum at B, then diminishing until it reaches zero at C, at which point it reverses direction and repeats the same pattern, CD, until it again reaches zero at E, completing one cycle. With three-phase electricity (C), three loads are transmitted, each 120° out of phase with the other. This form of current is particularly useful in industrial applications for running electric motors; it is also the standard supply for x-ray machines.