S1C8: Electric & Magnetic Energies

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a) Electric current

Electrons are going to remain centre stage again in this chapter. We will debut by focusing on the phenomenon of electric current, something our technological society makes a ubiquitous use of, more so than living organisms who tend to be powered by the electrochemical gradients we unravelled at the end of the previous chapter. You may want to read up about electromotive force in Section 7.e and the various electrical units in Section 6.e where the concepts of current, charge, power and resistance were briefly explained.

The underlying cause of electric current is a differential in electrical potential, something we should have come to expect by now since nature seeks to minimize potential energy when possible and a stream from one place to the other seems like the most direct way to solve for this. The difference in potential stems from the concentration of particles that are either positively or negatively charged as compared to a region not exhibiting the same concentration. Particles with positive charges would be cations (atoms or molecules stripped of one or more electrons) and those with negative charges would be electrons or anions (atoms or molecules with one or more extra electrons).

The charge is expressed in coulomb and the differential tends to dissipate through a flow of charged particles called electrical current towards areas with an opposite charge, this flow is expressed in ampere and can be thought as an intensity (the reason why current is represented by the letter “i”). In the case of a high concentration of electrons in an electrical circuit, those negatively charged particles will be channelled through a conductor such as a copper wire and travel towards a positively charge pole, so from negative to positive. This is mildly confusing because current is formally defined as heading from the positive to the negative, but electrons were not consulted it seems.

When the current is continuously flowing in one direction, it is called direct current – abbreviated as “DC”. This is the type of current delivered by batteries or solar power panels and used for electrolysis or nowadays in long distance transmission over the electricity grid. The other option is alternating current, shortened as “AC”, and like its name suggests it reverses direction at intervals with voltage following a sine wave function that can be broken down into positive and negative half-periods forming a cycle. This is the type of current we receive in our homes and use for our appliances because the voltage of AC current is much easier to modulate up or down via a transformer as compared to DC, although technological improvements are changing the landscape in this domain. For instance, long distance power transmission was historically based on AC because losses were lower with high voltage and low intensity current and such high voltage was easier to achieve with DC. The practical limitations having significantly eroded, if not disappeared, modern high voltage transmission lines now use DC. And by the way, don’t let the “war of the currents” between Edison and Westinghouse fool you, both direct and alternating currents are dangerous for biological beings like us given a high enough voltage or intensity.

However, there is one function AC can perform and DC cannot: the encoding and transmission of information. Indeed, the sine waves in AC can have three distinguishing properties. The first is their frequency, that is the number of cycles per second represented by the “hertz” unit. The second is their amplitude, which is determined by the peak height of the waveform corresponding to its maximum intensity. The third is the shape of the wave through phase modulation where the slope of the wave is the signal.

b) On the nature of electricity and electrical energy

At this stage, it is necessary to clarify what electrical current is and isn’t. This starts by going back to the concept of electrical charge, measured in coulomb. An electrical charge is not energy, it is a property of matter that makes particles susceptible to electromagnetic force. Hence, even though an electron always has the same charge, its energy level can change – generally through acceleration.

Consequently, electric current is a flow of charge, not a flow of energy, and electrons (or electrically charged entities) are not giving off their charge when they are made to work by being pushed through a load to carry out a specific task such as lighting a bulb or powering a TV screen. This explains why alternating current can be a thing: electrons going back and forth are a medium for delivering energy, not a source of energy being used up.

So what is electrical energy then? It is the energy embedded in the flow of charged particles, pushed by an electromotive force that is a function of the electrical current (the intensity) and electric potential (the voltage), just like the proton motive force pushes hydrogen cations through a proton gradient. Using the hydraulic analogy, the energy is not in the water molecules of the river, it is in their movement, carried along by the current of the river.

In mathematical terms, we have the power “P” being equal to the voltage “V” multiplied by the current or intensity “I”, a formula written as P = V*I. Power can be expressed in watts and, when multiplied by a unit of duration, this becomes an electrical energy unit such as the kilowatt hour or joule (1kWh = 3.6MJ).

c) Static electricity and electrical field

When electric charges accumulate in one location and are not being harmonized with their surrounding via an electric current, they can persist; this is called static electricity. Typically, it will be friction or another type of stress that will be responsible for charge separation and result in a localized accumulation of ions or electrons. For instance, when your hair has gained many electrons, it will experience this static electricity phenomenon and the extra electrons will repel each other, making your hair stand.

The imbalance can be rectified through an electric current or an electric discharge, which is essentially a very brief but intense flow of electrical charge along an electrical field. This type of discharge is what you occasionally experience when touching somebody else with one of your fingers and each of you happen to have a strong differential in electrical charge at the point of contact. Much more impressively, you can witness it in lightening. This electrical discharge is so intense that it superheats and expands the surrounding air, causing both incandescence (the light you see) and a shock wave (the thunder you hear).

The propensity of electrical charges to interact depends on the strength of their electrical field. One can think of the field as the theoretical zone of influence of the electrical charges and it is a function of both the distance between the charges and their magnitude – how highly positive or highly negative they are. The strength of the field is expressed in volt per meter (V/m) and increases proportionally to the magnitude and inversely with the square of the distance (gravity field also behaves this way), so if the distance doubles, then the strength of the field at this point further away would only be one quarter of its value at the original position.

d) Electron spin and magnetic moment

Electrons have another couple of important properties besides their charge: they have momentum around the nucleus and they rotate on themselves. This second behaviour is called spin and was already briefly mentioned in Section 7.g on quarks. Except electrons are point-like particles so they probably don’t actually rotate upon themselves in the physical sense we usually ascribe to a body like a planet. Regardless, spin is thought of and computed as a form of angular momentum, a quantity that doesn’t vary as long as no external force such as torque is applied to it – this makes it analogous to linear momentum and the first law of motion (refer to Section 6.d). Torque and angular momentum are important concepts in everything momentum and revolution so they are worth defining carefully.

Torque is best explained by using a couple of examples before jumping into definitions. When you push down on the horizontal lever of a doorknob, it will turn around its axis. The rotational component of this force is the torque, also called moment of force or just “moment”. When you turn a screwdriver or your fork in a plate of spaghetti, the torque is what produces torsion – and this is the etymological root of the name. If you think back of the lever, the further away from the centre of rotation you apply pressure, the more torque will be created even though the perpendicular element of the force applied is constant. If “F” is the force and “r” the radius or distance then the magnitude of the torque “τ” (the Greek letter tau) can be formulated as τ = F.r

If we think back about the laws of motion, we only discussed linear momentum but the mechanics obey the same principles when it comes to rotation and angular momentum is best described as the equivalent of this momentum but for a rotating body. The application of torque will translate into angular acceleration and an increase in angular momentum. The latter is a function of the distance from the centre of rotation (position vector), the rotation rate (velocity) and the mass of the body. When discussing particles such as quarks, by convention the angular momentum will have an “up” direction if its spin is positive, meaning it spins clockwise on its axis, and a “down” direction if it has a negative spin value (counterclockwise).

These concepts of angular momentum and torque carry over to electromagnetism. The motion of the electrons, whether spin (the rotation of particles upon themselves) or orbital (their revolution around the nucleus), results in a magnetic moment, a vector expressing the orientation and the strength of objects exerting a magnetic field. The greater the moment, the stronger the torque this object will experience in a magnetic field. This is a proportional relationship where the torque is the product of the magnetic moment and the value of the external magnetic field. Magnetic moment can be expressed in A.m² or alternatively in J/T where “T” stands for tesla, a measure of magnetic flux density. Magnetic flux density can be thought of as the measure of the amount of magnetic field passing through a particular area and is of course a function of the strength of the magnetic field in that area but also of its orientation. Quite the same way the amount of torque depends on the orientation of the force applied to a lever and is at its maximum when the force is perpendicular to it. For magnetic flux, it will be at its maximum when the surface is perpendicular to the field. If that helps, think of putting your hand in a current of water, you will notice the pressure to be at its maximum when you palm is perpendicular to the direction of the current.

e) Magnetic field and magnets

The logical question to ask now is therefore what magnetic fields are and how they differ from electrical fields. Magnetism compliments electrostatics in forming the electromagnetic interaction and together, the magnetic and electrical fields combine to form the electromagnetic field. Whereas the strength of an electric field depends on the magnitude of the charge of the particles from which it emanates and their location, that of a magnetic field is also a function of their velocity (direction and speed of the particles). So if “E” is the electrical field, “B” the magnetic field vector (that is the magnetic flux density mentioned in the previous paragraph), “v” is the velocity and “q” is the charge of the particle, then the electromagnetic force exerted by an electromagnetic field on the particle can be computed as F = qE + q(v x B) where “x” is the cross product of the vectors.

Figure 5: Interaction of charged particle in magnetic field

Credit: by Fjmelero on Wikipedia (CC BY-SA 3.0)

This may not be apparent from the equation, but the force that a charged particle moving through a magnetic field experiences is perpendicular to both its velocity and the field. Hence, the field is essentially the torque applied to the particle. This is illustrated in Figure 5.

In Figure 6, it is the magnetic field itself that is being visualized. In reality there is no finite number of field lines and the field is continuous. By convention, the magnetic field lines emerge from the north pole of a magnet, also called the positive pole, and are bound for the negative pole. Do note however that the positive and negative poles are colloquial expressions borrowed by analogy to an electrical field and the magnetic poles are not electrically charged.

Figure 6: magnetic pole model

Credit: by Geek3 on Wikipedia (CC BY-SA 3.0)

Any object producing a magnetic field is called a magnet. If you recall that a magnetic field is created by the motion of charged particles then it shouldn’t be surprising that running an electric current in a loop, such as a coil of wire, can create one; this is called an electromagnet and the field disappears when the current stops. This technology is used in hard disk drives, MRI machines and other electric devices.

However, when an object has been magnetized, it produces a persistent magnetic field. This is the magnet you might be familiar with and they are made of ferromagnetic materials such as iron, cobalt and nickel. To understand the emergence of a persistent magnetic field in these materials, we must go back to their sub-atomic make-up.

In normal circumstances, the magnetic moments caused by the spin of electrons tend to cancel each other out more or less completely, although there is still some magnetic field created by the orbital angular momentum – that created by the electrons travelling around the nucleus. This is always the case when the electron shells are filled – yes, the same shells involved in covalent bonds we discussed in Section 2.d. You may want to read back on this but technicality it isn’t really consequential in terms of understanding the phenomenon of ferromagnetism. So, in certain chemical elements with an unfilled shelf, the electrons’ spin tends to align with each other, a consequence of the respective magnetic field they create and the ensuing application of torque. The result is an increase in the total magnetic moment of the atom and, if the interaction with neighbouring atoms is strong enough, they will also align themselves and remain so. The combination of the internal structure of ferromagnetic materials and the microscopic arrangement of these atoms in the materials is what makes it possible for them to become permanent magnets.

In electromagnets, the electrical current is often made to circulate around a magnetic core to enhance the strength of the field. This configuration is what creates the Earth’s magnetic field: it has an iron-rich core and electrically conducing molten materials flowing in the outer-core that create convection currents. The boundary of this field bears the name of magnetosphere and the magnetic field repulsion is what prevents smalls parts of the sun’s own magnetic field detached from its corona by the solar wind from ejecting part of our planet’s atmosphere through pressure.

In addition, the Earth’s magnetic field also deflects high-energy charged particles called cosmic rays representing a health threat under significant exposure because they carry sufficient energy to break chemical bounds and ionize atoms and molecules, thus potentially damaging living cells. Put together, this suggests the existence of a magnetic field is helpful to the emergence of complex life on a planet although not to the same degree as the existence of the atmosphere itself and its retention by strong-enough gravitational forces.

f) Trivia – the Magnetic North

In English, the etymology of lodestone is “leading stone”. This material is a type of magnetite, a naturally-occurring magnet, and its name originates from its use as the needle of the first magnetic compasses.

By convention, on account of the torque exacted on it by the Earth’s magnetic field, the north end of the needle of a compass points towards the “magnetic north”. Except that the field line going through the north pole of the compass should be pointing towards the south pole of the Earth’s magnetic pole, and of course that is what it does! Yes, you read this correctly. This means what we call the North geomagnetic pole is in reality the South pole of our planet’s magnetic field. And vice versa.

Unlike the geographic North Pole and South Pole which are fixed points defined as the location where the Earth’s axis of rotation intersects the surface of the planet in the northern and southern hemispheres, respectively, the location of magnetic poles shifts over time as a result of the movement of the magnetic materials in the outer core. Thus, it would not be surprising if the location of said north and south magnetic poles were not symmetrical, and indeed they are not. In 2010, it was 85.020°N, 132.834°W for the North (of course) and 64.432°S, 137.325°E for the South, so quite a large difference in terms of latitude. Since then the magnetic South Pole has varied dramatically but its northern counterpart has been racing back south towards Siberia.

And then, the mother of all magnetic pole movement: geomagnetic reversal. This is essentially a sudden flip in polarity, estimated to take between 1,000 and 10,000 years and taking place on average twice every million years in the last 80 million years or so. Nothing mystical happening there, it is all the result of the dynamics in the interior of our planet. Evidence of such reversals can be found in the orientation of magnetic materials in sedimentary rocks, lodestone for the ages.