IB Physics 2015 Higher level Paper 2 Question 3

Question: Students are expected to provide a definition of an electromotive force.

Mark scheme: 
The work done per unit charge in moving a quantity of charge completely around a circuit.
OR the power delivered per unit current.
OR work done per unit charge made available by a source.

Comments: 

As an example, the question could be phrased as “define the electromotive force (emf) of an ideal battery” instead of simply “define electromotive force.” The electromotive force of a real battery is different from an ideal battery that has no internal resistance. On the other hand, it is possible to have an induced electromotive force in the electrical circuit due to a metal wire moving perpendicularly across the Earth’s magnetic field. Thus, the question should be more precise.

This mark scheme is slightly different from Tsokos’ (2008) definition of electromotive force: “In the case of the battery, the ratio of work done by non-electrical forces, W, to a quantity of charge q that moves from one terminal of the battery to the other is called the emf of the battery (p. 319).” That is, the mark scheme does not include the nature of forces (non-electrical) involved in the work done. For example, Lerner (1996) writes that “the external work per unit charge that must be expended to produce an increase ∆V in the electric potential of the charge is called the electromotive force (Lerner, 1996, p. 727).” He also explains that the external force that acts on the unit charge in producing an electromotive force can be a non-conservative force, whereas the electric force that opposes the external force is a conservative force. (Similarly, the force in which your arm raises an object is non-conservative, but the gravitational force that opposes this external force is conservative.)

In addition, the mark scheme does not specify the condition “open circuit” or “no current is being drawn” that can be found in the mark schemes of other examination boards. Importantly, in an article titled Electromotive force, potential difference, and voltage, Page (1977) writes that “[i]n an open circuit, the electromotive force is measured by the potential difference that it maintains. In a closed circuit, it is equal to the instantaneous power developed, divided by the value of the current in the circuit (p. 979).” Mathematically, the effective electromotive force (V) of a real battery can be calculated by the equation V = E – Ir; E is the maximum voltage across the output terminals when no electric current flows through the real battery, I is the electric current that flows through the battery, and r is the internal resistance of the battery. Therefore, the effective electromotive force of an electrical source is dependent on whether the electrical circuit is open or closed.

Feynman Insights?:

Currently, there is no agreement on the definition of electromotive force. In The Feynman Lectures on Physics, it is stated that “the emf is defined as the tangential force per unit charge in the wire integrated over length, once around the complete circuit (Feynman et al., 1964, section 16–1 Motors and generators).” In short, the electromotive force (Emf) around a closed circuit is the line integral of the electric field (E) in the wire, and it can be mathematically expressed as  Emf = ∫ E · ds. However, Feynman’s definition can be misleading because it has a connotation that the electromotive force is a kind of force. Thus, one may prefer the term electromotive potential or electromotive voltage (Legault & Peschard, 2001). 

Furthermore, Feynman adds that “[w]e have already defined the emf in a conducting circuit as the total accumulated force on the charges throughout the length of the loop. More specifically, it is the tangential component of the force per unit charge, integrated along the wire once around the circuit. This quantity is equal, therefore, to the total work done on a single charge that travels once around the circuit (Feynman et al., 1964, section 17–1 The physics of induction).” Importantly, Feynman clarifies that the electromotive force is the total work done on a unit charge in the electrical circuit. Historically speaking, Volta defines the electromotive force as a nonelectrostatic action on charge-carriers in the electrical circuit, that causes unlike charges to remain separated. However, current physicists redefine the term electromotive force as the total work done (measured in joules) instead of a force (measured in newtons).

Note: 

Page also mentions that “[i]n the case of a battery, its electromotive force can be determined by an open-circuit measurement of the potential difference between its terminals; in the case of a series-wound generator (converting mechanical energy to electric energy), the emf is a function of the load current, and is ideally zero under open-circuit conditions (Page, 1977, p. 979).” 

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.
2. Legault, N., & Peschard, D. (2001). Concerning the electromotive force (or emf). The Physics Teacher, 39(2), 69. 
3. Lerner, L. S. (1996). Physics for scientists and engineers. Boston, MA: Jone and Barlett. 
4. Page, C. H. (1977). Electromotive force, potential difference, and voltage. American Journal of Physics, 45(10), 978-80. 
5. Tsokos, K. A. (2008). Physics for the IB Diploma (5th ed.). Cambridge: Cambridge University Press.