Book contents
- Frontmatter
- PREFACE
- Contents
- ELECTRICITY AND MAGNETISM
- PRELIMINARY
- PART I ELECTROSTATICS
- CHAPTER I DESCRIPTION OF PHENOMENA
- CHAPTER II ELEMENTARY MATHEMATICAL THEORY OF ELECTRICITY
- CHAPTER III SYSTEMS OF CONDUCTORS
- CHAPTER IV GENERAL THEOREMS
- CHAPTER V MECHANICAL ACTION BETWEEN ELECTRIFIED BODIES
- CHAPTER VI POINTS AND LINES OF EQUILIBRIUM
- CHAPTER VII FORMS OF EQUIPOTENTIAL SURFACES AND LINES OF FLOW
- CHAPTER VIII SIMPLE CASES OF ELECTRIFICATION
- CHAPTER IX SPHERICAL HARMONICS
- CHAPTER X CONFOCAL SURFACES OF THE SECOND DEGREE
- CHAPTER XI THEORY OF ELECTRIC IMAGES
- CHAPTER XII CONJUGATE FUNCTIONS IN TWO DIMENSIONS
- CHAPTER XIII ELECTROSTATIC INSTRUMENTS
- PART II ELECTROKINEMATICS
- Plate section
CHAPTER III - SYSTEMS OF CONDUCTORS
Published online by Cambridge University Press: 05 July 2011
- Frontmatter
- PREFACE
- Contents
- ELECTRICITY AND MAGNETISM
- PRELIMINARY
- PART I ELECTROSTATICS
- CHAPTER I DESCRIPTION OF PHENOMENA
- CHAPTER II ELEMENTARY MATHEMATICAL THEORY OF ELECTRICITY
- CHAPTER III SYSTEMS OF CONDUCTORS
- CHAPTER IV GENERAL THEOREMS
- CHAPTER V MECHANICAL ACTION BETWEEN ELECTRIFIED BODIES
- CHAPTER VI POINTS AND LINES OF EQUILIBRIUM
- CHAPTER VII FORMS OF EQUIPOTENTIAL SURFACES AND LINES OF FLOW
- CHAPTER VIII SIMPLE CASES OF ELECTRIFICATION
- CHAPTER IX SPHERICAL HARMONICS
- CHAPTER X CONFOCAL SURFACES OF THE SECOND DEGREE
- CHAPTER XI THEORY OF ELECTRIC IMAGES
- CHAPTER XII CONJUGATE FUNCTIONS IN TWO DIMENSIONS
- CHAPTER XIII ELECTROSTATIC INSTRUMENTS
- PART II ELECTROKINEMATICS
- Plate section
Summary
On the Superposition of Electrical Systems
84.] Let E1 be a given electrified system of which the potential at a point P is V1, and let E2 be another electrified system of which the potential at the same point would be V2 if E1 did not exist. Then, if E1 and E2 exist together, the potential of the combined system will be V1 + V2.
Hence, if V be the potential of an electrified system E, if the electrification of every part of E be increased in the ratio of n to 1, the potential of the new system nE will be nV.
Energy of an Electrified System
85.] Let the system be divided into parts, A1, A2, &c. so small that the potential in each part may be considered constant throughout its extent. Let e1, e2, &c. be the quantities of electricity in each of these parts, and let V1, V2, &c. be their potentials.
If now e1 is altered to ne1, e2 to ne2, &c. then the potentials will become nV1, nV2, &c.
Let us consider the effect of changing n into n + dn in all these expressions. It will be equivalent to charging A1 with a quantity of electricity e1dn, A2 with e2dn, &c. These charges must be supposed to be brought from a distance at which the electrical action of the system is insensible.
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- A Treatise on Electricity and Magnetism , pp. 88 - 97Publisher: Cambridge University PressPrint publication year: 2010