Electric current (A flow of electrons or positive charges?)

Question: What do you understand by the term electric current? OR Explain what is meant by an electric current.

In a study conducted by Garnett and Treagust (1992), students studying both physics and chemistry were more confused about the concept of electric currents in metallic conductors as compared to students who were only studying chemistry. They propose that the physics syllabus should adopt the electron flow model of electric current in metallic conductors because some students had conceptual problems with the different conventions used in chemistry and physics. On the contrary, Arons (1990) argues that the positive current convention should be maintained in physics for the following four reasons: “(1) the definitions of electric field strength and potential difference; (2) the treatment of capacitive and inductive circuit elements; (3) all the standard mnemonics of electromagnetism and the Maxwell’s equations; and (4) the standard notations in diagrams of electronic circuits (p. 179).” However, electric current can be defined as a flow of charge carriers such as electrons and holes depending on the context.

How would Feynman answer?

Feynman might discuss charge carriers, nature of the electric current, and problems of defining the electric current as shown below.

1. Charge carriers: An important feature of a definition of electric current is the charge carriers. For instance, Feynman states that “[e]lectric currents are electrons or other charges in motion with a net drift or flow (Feynman et al., 1964, section 13–2 Electric current; the conservation of charge).” That is, an electric current is a net drift or flow of charge carriers such as electrons. In addition, this is dependent on the context (or a conducting medium) such as a copper wire or metallic conductor. Thus, Feynman mentions that “[i]n a normal conductor, like copper, the electric currents come from the motion of some of the negative electrons — called the conduction electrons — while the positive nuclear charges and the remainder of the electrons stay fixed in the body of the material (Feynman et al., 1964, section 13–6 The relativity of magnetic and electric fields).”

In general, electric charge can be positive and negative, and charge carriers may include electrons and holes. Therefore, Feynman elaborates that “[o]ne can also have both holes and electrons together. If there are not too many, they will all go their way independently. With an electric field, they will all contribute to the current. For obvious reasons, electrons are called the negative carriers and the holes are called the positive carriers. We have so far considered that electrons are put into the crystal from the outside, or are removed to make a hole. It is also possible to ‘create’ an electron-hole pair by taking a bound electron away from one neutral atom and putting it some distance away in the same crystal. We then have a free electron and a free hole, and the two can move about as we have described (Feynman et al., 1966, section 14–1 Electrons and holes in semiconductors).” In short, the charge carriers include electrons and holes in the context of semiconductors.

On the other hand, there are also electric currents in the earth’s atmosphere. In fact, Feynman mentions that “[d]ue to the air currents, ions, and water drops on ice particles in a thunderstorm, positive and negative charges are separated. The positive charges are carried upward to the top of the cloud, and the negative charges are dumped into the ground in lightning strokes. The positive charges leave the top of the cloud, enter the high-altitude layers of more highly conducting air, and spread throughout the earth. In regions of clear weather, the positive charges in this layer are slowly conducted to the earth by the ions in the air — ions formed by cosmic rays, by the sea, and by man’s activities. The atmosphere is a busy electrical machine! (Feynman et al., 1964, section 9–5 The mechanism of charge separation).” In other words, we should not only visualize electric currents in terms of electric circuits and metallic conductors.

2. Nature of electric current: In textbooks, a simple definition of electric current is a flow of electrons. During a BBC interview, Feynman (1994) explains that “[y]ou can imagine the city electricity as being like a water system if you like. You can visualize the electrons going in pipes all over the place, with a big pump at one end. In fact, look at any book and they’ll tell you that the voltage is the pressure and the amperage is the amount of flow (p. 135).” Essentially, electric current is about the amount of flow. Importantly, Feynman also provides a good analogy in which the electric current is like the flow of water and the potential difference is similar to the pressure difference. However, electric current could be more precisely defined as the rate of flow of charge carriers instead of simply the flow of charge carriers.

Mathematically, Feynman states that “the current I can be written as ρ₋vA (Feynman et al., 1964, section 13–6 The relativity of magnetic and electric fields).” Note that ρ₋ refers to charge density of the conduction electrons, A refers to the area of a cross-section of the wire, and v is the velocity of the conduction electrons. Simply phrased, the rate of flow is dependent on the velocity of charge carriers. In addition, Feynman mentions that “[t]he total charge passing per unit time through any surface S is called the electric current, I. It is equal to the integral of the normal component of the flow through all of the elements of the surface: I = ʃS j · n dS (Feynman et al. 1964, section 13–2 Electric current; the conservation of charge).” This provides another mathematical definition of electric current as compared to I = dq/dt which means the instantaneous rate of flow of electric charge, q.

Better still, electric current can be defined as a rate of flow of ‘free’ electrons due to a potential difference across the ends of the metallic conductor. Importantly, it is the electric field that causes the flow of electrons in a copper wire. In Feynman’s words, “in an atom with three protons in the nucleus exchanging photons with three electrons – a condition called a lithium atom - the third electron is further away from the nucleus than the other two (which have used up the available space), and exchanges fewer photons. This causes the electron to easily break away from its own nucleus under the influence of photons from other atoms. A large number of such atoms close together easily lose their individual third electrons to form a sea of electrons swimming around from atom to atom. This sea of electrons reacts to any small electrical force (photons), generating a current of electrons - I am describing lithium metal conducting electricity (Feynman, 1985, p. 113).” In essence, the flow of electrons is due to the presence of the electric field and it is mediated by photons.

3. Problems of Defining electric current: The definition of electric current has several definitional problems which may not be easily resolved. Firstly, electric current is sometimes defined as “the rate of flow of electric charge, I = q/t” and electric charge is defined by the equation, “electric charge (q) = electric current (I) × the duration of time for which it flows (t).” This suggests a problem of circularity in which both electric current and electric charge are defined by using the same equation. However, this circularity problem should not be resolved by considering electric current to be a fundamental concept and thus it is indefinable or it cannot be defined in terms of simpler, more basic concepts.

Another problem is that the Poynting theory pertaining to the flow of energy in a wire seems “crazy” to Feynman. In his own words, “[w]e ask what happens in a piece of resistance wire when it is carrying a current. Since the wire has resistance, there is an electric field along it, driving the current. Because there is a potential drop along the wire, there is also an electric field just outside the wire, parallel to the surface. There is, in addition, a magnetic field which goes around the wire because of the current. The E and B are at right angles; therefore there is a Poynting vector directed radially inward, as shown in the figure. There is a flow of energy into the wire all around. It is, of course, equal to the energy being lost in the wire in the form of heat. So our “crazy” theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside… the theory says that the electrons are really being pushed by an electric field, which has come from some charges very far away, and that the electrons get their energy for generating heat from these fields (Feynman et al. 1964 section 27-5 Examples of energy flow).” Intuitively speaking, Feynman feels that the theory is incomplete because it does not seem to make sense that the field energy could flow from the battery to infinity, and then back into the wire as suggested by Poynting vector.

Furthermore, Feynman mentions that “if currents are made to go through a piece of material obeying Ohm’s law, the currents distribute themselves inside the piece so that the rate at which heat is generated is as little as possible. Also, we can say (if things are kept isothermal) that the rate at which energy is generated is a minimum. Now, this principle also holds, according to classical theory, in determining even the distribution of velocities of the electrons inside a metal which is carrying a current. The distribution of velocities is not exactly the equilibrium distribution because they are drifting sideways. The new distribution can be found from the principle that it is the distribution for a given current for which the entropy developed per second by collisions is as small as possible. The true description of the electrons’ behavior ought to be by quantum mechanics, however. The question is: Does the same principle of minimum entropy generation also hold when the situation is described quantum-mechanically? I haven’t found out yet (Feynman et al., section 19–2 A note added after the lecture).” Simply phrased, the theory of electric current is also incomplete from a perspective of quantum mechanics. 

       In summary, a comprehensive definition of electric current is a rate of flow of free electrons due to a potential difference (or electric field) across the ends of the conductor, under constant circuit conditions. More importantly, Feynman would discuss charge carriers, the nature of electric current in different contexts and equations, as well as definitional problems of electric current.

Note:

In Feynman Lectures on Computation, Feynman (1996) explains that “[g]ood conductors have a plentiful supply of free electrons under normal conditions, the band gap energy being tiny or non-existent (filled and conduction bands can even overlap) (p. 214).”

References:
1. Arons, A. B. (1990). A guide to introductory physics teaching. New York: John Wiley & Sons.
2. Feynman, R. P. (1985). QED: The Strange Theory of Light and Matter. Princeton: Princeton Scientific Library.
3. Feynman, R. P. (1994). No Ordinary Genius: The Illustrated Richard Feynman. New York: W. W. Norton & Company.
4. Feynman, R. P. (1996). Feynman lectures on computation. Reading, Massachusetts: Addison-Wesley. 
5. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.
6. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol III: Quantum Mechanics. Reading, MA: Addison-Wesley.
7. Garnett, P. J., & Treagust, D. F. (1992). Conceptual difficulties experienced by senior high school students of electrochemistry: Electric circuits and oxidation-reduction equations. Journal of Research in Science Teaching, 29(2), 121-142.