Abstract
In this chapter we introduce and develop the properties of the electrostatic scalar potential. This is the first of two potentials in classical field theory both of which appeared in the original work by Maxwell. We will find that these potentials are central to the theory replacing the fields in advanced topics. The fact that a scalar potential exists follows immediately from the second electrostatic field equation, that for the curl of \(\vec{E}\). The electrostatic force is conservative and is, therefore, obtainable from a potential energy.
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Notes
- 1.
The unit of the volt honors Count Alessandro Volta who developed the first electrochemical cell (see Sect. 1.8).
- 2.
We have designated the total mechanical energy of the charge as \(\mathcal{H}\) rather than E to avoid confusion with the designation for the field, and because \(\mathcal{H}\) is the standard designation of the Hamiltonian, which, for conservative systems, is the total energy.
- 3.
The quadrupole moment is a tensor.
- 4.
The solution for φ in (4.8) is unique (see Appendices).
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© 2012 Springer-Verlag Berlin Heidelberg
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Helrich, C.S. (2012). The Scalar Potential. In: The Classical Theory of Fields. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23205-3_4
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DOI: https://doi.org/10.1007/978-3-642-23205-3_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23204-6
Online ISBN: 978-3-642-23205-3
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