Energy transfer in electrical circuits: A qualitative account

Aristotle, Physics (Peripatetic P. Grinnvel, IA, 1980), Vol. II, Chap. 3.

We address instruction at the level of D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (Wiley, New York, 2001). Most textbooks ignore the issue of energy transfer in dc electrical circuits.

D. Halliday and R. Resnick, Fundamentals of Physics (Wiley, New York, 1988), p. 651.

R. Feynman, R. Leighton, and M. Sands, Feynman Lectures on Physics (Addison–Wesley, Reading, MA, 1964), Vol. 2, pp. 27–28.

A. Sommerfeld, Electrodynamics (Academic, New York, 1952), pp. 125–130.

J. D. Jackson extended the axially symmetrical problem of Sommerfeld to the closed circuit of the same symmetry and provided a comprehensive and exhaustive analytic solution of this case. See

J. D.

 

Jackson

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See also

J. A.

Hernandes

and

A. K. T.

Asis

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O.

Jefimenko

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See

N.

Preyer

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H. Härtel, “A qualitative approach to electricity,” Institute for Research on Learning, Report #87-0001, September 1987.

R. Chabay and B. Sherwood, Matter & Interactions: Electric & Magnetic Interactions (Wiley, New York, 2002); B. A. Sherwood, and R. W. Chabay, “A unified treatment of electrostatics and circuits,” 〈http://www4.ncsu.edu/∼rwchabay/mi/circuit.pdf〉.

This gradient results in feedback during the transient process, which ultimately produces the steady state in the circuit. The steady current satisfying Kirchhoff laws (charge conservation at the nodes and energy transformation rate, as determined by resistivity of circuit fragments) requires a special distribution of the surface charge producing a particular pattern of the electric field.

These boundary conditions follow from the straightforward application of Gauss’s and Stokes’s theorems.

Many educators would prefer to simply state that the battery drives conventional current through the battery from − to +, opposite to the Coulomb electric field between the terminals. This statement, however, appears to be highly confusing to a novice. Instead, we could say that the process within the battery causes the separation of electric charges, which could be represented by an efficient current in the direction opposite to the Coulomb force within the battery. The efficient current is an imaginary current, which would close the circuit in accord with charge conservation. Actually, no charge makes a closed loop in the circuit, but the constantly occurring redistribution of the atomic charges in the chemical reactions (decreasing the internal electric energy of the products) causes the gathering of electrons on the terminal of the battery. This process, although essentially quantum (tunneling), deserves a qualitative explanation.

Except that there must be some charge on the bends of the wire to turn the electrons.

We should not forget that we discuss only the classical picture in an introductory course. Quantum theory changes the nature of the statement regarding the “inertial movement” of the conduction electrons. The notion of inertial movement of electrons is, however, consistent with the introductory instruction in mechanics.

An explanation of the Poynting vector appropriate for introductory students is usually provided in the context of energy transport by electromagnetic waves. See, for example, D. Halliday, R. Resnik, and J. Walker, Fundamentals of Physics (Wiley, New York, 2001), 6th ed., pp. 809–810 or F. W. Sears, M. W. Zemansky, and H. D. Young, University Physics (Addison–Wesley, Reading, MA, 1982), 6th ed., pp. 700–703.

At the college level, the Poynting vector is usually introduced without the vector product. See, for example, F. W. Sears, M. W. Zemansky, and H. D. Young, College Physics (Addison–Wesley, Reading, MA, 1977), 4th ed., pp. 571–572.

See for example,

R. J.

 

Osborne

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T. A.

Borges

and

J. K.

Gilbert

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