# Pre-Quantum Electrodynamics
Author: Jean-Sébastien Caux

##### Comments on the Electrostatic Potential
ems.es.ep.c

(i) The name. It's fine by me. I don't see what Griffiths' problem is (more precisely: Griffiths sees a problem where there isn't one). (ii) Advantages. In view of \ref{Gr(2.23)}, it's much simpler to first calculate the potential (which is a scalar field), and to then calculate the electrostatic field (which is a vector field).

But how can a vector field (3 components, so 3 functions) be generated by a scalar field (one component, so one function) ? Griffiths mentions that \ref{Gr(2.20)} explains this. For curious students, resolve this paradox: \ref{Gr(2.20)}, when written out in components, gives 3 functional constraints on the electric field. We might thus think that we have no freedom left. How come we thus end up with a 'one function' degree of freedom ? (iii) The reference point. Not a problem to put it at infinity if we only use charge distributions which don't go to infinity. Otherwise, choose a different point! (iv) Superposition principle. Already mentioned. (v) Units. Newton-meters per coulomb or joules per coulomb, which is called a volt. In the SI system where the ampere is a base unit, a volt is a \(kg m^2/s^3 A\).

Author: Jean-Sébastien Caux

Created: 2022-02-08 Tue 06:55

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