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7 - Induced Currents and Charges in Conductors

Published online by Cambridge University Press:  16 October 2026

Jene A. Golovchenko
Affiliation:
Harvard University, Massachusetts
Edlyn V. Levine
Affiliation:
Harvard University, Massachusetts
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Summary

This chapter analyzes how conductors respond to external charges through induced charge densities, screening, and currents. It first reviews the picture of mobile and bound charge in a metal and derives the screening time by combining Ohm’s law with the continuity equation and Gauss’s law. The chapter then treats screening of charges outside a conductor, enforcing boundary conditions on the electric field and surface charge, and develops integral representations for the fields using the near-field approximation and surface charge distributions. These ideas are systematized with the Green’s function method for electrostatics, including Fourier-space constructions and the solution of canonical half-space and planar-boundary problems. Green’s theorem is then used to formulate general boundary value problems for the scalar potential in terms of Green’s functions, free charge, and induced surface charge on conducting bodies. Finally, the chapter derives and interprets the Shockley–Ramo theorem, which expresses the current induced on electrodes by moving charges, and applies it to parallel-plate capacitors and simple detector circuits.

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